1.3 Övningar
Sommarmatte 1
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| Rad 1: | Rad 1: | ||
| + | __NOTOC__ | ||
| ==Övning 1.3:1== | ==Övning 1.3:1== | ||
| Rad 4: | Rad 5: | ||
| Beräkna | Beräkna | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">2^3\cdot3^2</td> | + | <td class="ntext" width="25%">2^3\cdot3^2</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">3^5\cdot9^{-2}</td> | + | <td class="ntext" width="25%">3^5\cdot9^{-2}</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">(-5)^3</td> | + | <td class="ntext" width="25%">(-5)^3</td> |
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">$\left(\displaystyle \frac{2}{3}\right)^{-3}$</td> | + | <td class="ntext" width="25%">$\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 22: | Rad 22: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">$\textrm{a) }$</td> | + | <td class="ntext">a)</td> |
| - | <td class="ntext">72</td> | + | <td class="ntext" width="25%">72</td> |
| - | <td class="ntext">$\textrm{b) }$</td> | + | <td class="ntext">b)</td> |
| - | <td class="ntext">3</td> | + | <td class="ntext" width="25%">3</td> |
| - | <td class="ntext">$\textrm{c) }$</td> | + | <td class="ntext">c)</td> |
| - | <td class="ntext">-125</td> | + | <td class="ntext" width="25%">-125</td> |
| - | <td class="ntext">$\textrm{d) }$</td> | + | <td class="ntext">d)</td> |
| - | <td class="ntext">\displaystyle \frac{27}{8}</td> | + | <td class="ntext" width="25%">\displaystyle \frac{27}{8}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 41: | Rad 40: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_1a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_1b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_1c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:1_3_1d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_1d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 73: | Rad 100: | ||
| Skriv som en potens av 2 | Skriv som en potens av 2 | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext"> 2\cdot4\cdot8</td> | + | <td class="ntext" width="33%">2\cdot4\cdot8</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">0,25</td> | + | <td class="ntext" width="33%">$0{,}25$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">$\textrm{1}$</td> | + | <td class="ntext" width="33%">1</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 89: | Rad 115: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">2^6</td> | + | <td class="ntext" width="33%">2^6</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">2^{-2}</td> | + | <td class="ntext" width="33%">2^{-2}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">2^0</td> | + | <td class="ntext" width="33%">2^0</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 106: | Rad 131: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_2a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_2a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_2b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_2b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_2c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_2c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 131: | Rad 177: | ||
| Skriv som en potens av 3 | Skriv som en potens av 3 | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">\displaystyle \frac{1}{3}</td> | + | <td class="ntext" width="20%">\displaystyle \frac{1}{3}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">243</td> | + | <td class="ntext" width="20%">243</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">9^2</td> | + | <td class="ntext" width="20%">9^2</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">\displaystyle \frac{1}{27}</td> | + | <td class="ntext" width="20%">\displaystyle \frac{1}{27}</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">\displaystyle \frac{3}{9^2}</td> | + | <td class="ntext" width="20%">\displaystyle \frac{3}{9^2}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 151: | Rad 196: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">3^{-1}</td> | + | <td class="ntext" width="20%">3^{-1}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">3^5</td> | + | <td class="ntext" width="20%">3^5</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">3^4</td> | + | <td class="ntext" width="20%">3^4</td> |
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">3^{-3}</td> | + | <td class="ntext" width="20%">3^{-3}</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">3^{-3}</td> | + | <td class="ntext" width="20%">3^{-3}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 172: | Rad 216: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_3a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_3b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_3c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:1_3_3d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:1_3_3e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_3e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 211: | Rad 290: | ||
| Beräkna | Beräkna | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">2^{9}\cdot2^{-7}</td> | + | <td class="ntext" width="33%">2^{9}\cdot2^{-7}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">3^{13}\cdot9^{-3}\cdot27^{-2}</td> | + | <td class="ntext" width="33%">3^{13}\cdot9^{-3}\cdot27^{-2}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}</td> | + | <td class="ntext" width="33%">\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}</td> | + | <td class="ntext" width="33%">2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">625\cdot(5^{8}+5^{9})^{-1}</td> | + | <td class="ntext" width="33%">625\cdot(5^{8}+5^{9})^{-1}</td> |
| - | <td class="ntext"></td> | + | |
| - | <td class="ntext"></td> | + | |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 236: | Rad 311: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">4</td> | + | <td class="ntext" width="33%">4</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">3</td> | + | <td class="ntext" width="33%">3</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">625</td> | + | <td class="ntext" width="33%">625</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">16</td> | + | <td class="ntext" width="33%">16</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">\displaystyle \frac{1}{3750}</td> | + | <td class="ntext" width="33%">\displaystyle \frac{1}{3750}</td> |
| - | <td class="ntext"></td> | + | |
| - | <td class="ntext"></td> | + | |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 262: | Rad 333: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_4a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_4b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_4c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:1_3_4d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:1_3_4e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_4e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 301: | Rad 407: | ||
| Beräkna | Beräkna | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">4^{1/2}</td> | + | <td class="ntext" width="33%">4^{1/2}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">4^{-1/2}</td> | + | <td class="ntext" width="33%">4^{-1/2}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">9^{3/2}</td> | + | <td class="ntext" width="33%">9^{3/2}</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">\left(47^{2/3} \right) ^{3}</td> | + | <td class="ntext" width="33%">\left(47^{2/3} \right) ^{3}</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">3^{1,4}\cdot3^{0,6}</td> | + | <td class="ntext" width="33%">$3^{1{,}4}\cdot3^{0{,}6}$</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">$\left( 125 ^{1/3} \right)^2\cdot \left( 27^{1/3} \right)^{-2}\cdot9^{1/2}$</td> | + | <td class="ntext" width="33%">$\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 326: | Rad 430: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">2</td> | + | <td class="ntext" width="33%">2</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">\displaystyle \frac{1}{2}</td> | + | <td class="ntext" width="33%">\displaystyle \frac{1}{2}</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">27</td> | + | <td class="ntext" width="33%">27</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">2209</td> | + | <td class="ntext" width="33%">2209</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">9</td> | + | <td class="ntext" width="33%">9</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">\displaystyle \frac{25}{3}</td> | + | <td class="ntext" width="33%">\displaystyle \frac{25}{3}</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 352: | Rad 454: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_5a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_5b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_5c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:1_3_5d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:1_3_5e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning f </div> | + | <div class=NavHead>Lösning f) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga f<br \>[[Bild:1_3_5f.gif]] | + | Lösning till delfråga f) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_5f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| Rad 397: | Rad 541: | ||
| Avgör vilket tal som är störst av | Avgör vilket tal som är störst av | ||
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">256^{1/3} och 200^{1/3}</td> | + | <td class="ntext" width="33%">$256^{1/3}\ och \ 200^{1/3}$</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">0,5^{-3} och 0,4^{-3}</td> | + | <td class="ntext" width="33%">$0{,}5^{-3}\ och \ 0{,}4^{-3}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">0,2^5 och 0,2^{7}</td> | + | <td class="ntext" width="33%">$0{,}2^5\ och \ 0{,}2^{7}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">400^{1/3} och $\left(5^{1/3}\right)^{4}$</td> | + | <td class="ntext" width="33%">$400^{1/3}\ och \ \bigl(5^{1/3}\bigr)^{4}$</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">125^{1/2} och 625^{1/3}</td> | + | <td class="ntext" width="33%">$125^{1/2}\ och \ 625^{1/3}$</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">2^{56} och 3^{40}</td> | + | <td class="ntext" width="33%">$2^{56}\ och \ 3^{40}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 422: | Rad 564: | ||
| <div class=NavHead>Facit </div> | <div class=NavHead>Facit </div> | ||
| <div class=NavContent> | <div class=NavContent> | ||
| - | Facit till alla delfrågorna<br \> | + | Facit till alla delfrågor<br \> |
| <table width="100%" cellspacing="10px"> | <table width="100%" cellspacing="10px"> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">a)</td> | <td class="ntext">a)</td> | ||
| - | <td class="ntext">256^{1/3}>200^{1/3}</td> | + | <td class="ntext" width="33%">256^{1/3}>200^{1/3}</td> |
| <td class="ntext">b)</td> | <td class="ntext">b)</td> | ||
| - | <td class="ntext">0,4^{-3}>0,5^{-3}</td> | + | <td class="ntext" width="33%">$0{,}4^{-3}>0{,}5^{-3}$</td> |
| <td class="ntext">c)</td> | <td class="ntext">c)</td> | ||
| - | <td class="ntext">0,2^{5}>0,2^{7}</td> | + | <td class="ntext" width="33%">$0{,}2^{5}>0{,}2^{7}$</td> |
| </tr> | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| <td class="ntext">d)</td> | <td class="ntext">d)</td> | ||
| - | <td class="ntext">$\left(5^{1/3}\right)^{4}>400^{1/3}$</td> | + | <td class="ntext" width="33%">$\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$</td> |
| <td class="ntext">e)</td> | <td class="ntext">e)</td> | ||
| - | <td class="ntext">125^{1/2}>625^{1/3}</td> | + | <td class="ntext" width="33%">125^{1/2}>625^{1/3}</td> |
| <td class="ntext">f)</td> | <td class="ntext">f)</td> | ||
| - | <td class="ntext">$3^{30}>2^{56}$</td> | + | <td class="ntext" width="33%">$3^{40}>2^{56}$</td> |
| </tr> | </tr> | ||
| <tr><td height="5px"/></tr> | <tr><td height="5px"/></tr> | ||
| Rad 448: | Rad 588: | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning a </div> | + | <div class=NavHead>Lösning a) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga a<br \>[[Bild:1_3_6a.gif]] | + | Lösning till delfråga a) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6a.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning b </div> | + | <div class=NavHead>Lösning b) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga b<br \>[[Bild:1_3_6b.gif]] | + | Lösning till delfråga b) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6b.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning c </div> | + | <div class=NavHead>Lösning c) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga c<br \>[[Bild:1_3_6c.gif]] | + | Lösning till delfråga c) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6c.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning d </div> | + | <div class=NavHead>Lösning d) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga d<br \>[[Bild:1_3_6d.gif]] | + | Lösning till delfråga d) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6d.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning e </div> | + | <div class=NavHead>Lösning e) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga e<br \>[[Bild:1_3_6e.gif]] | + | Lösning till delfråga e) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6e.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
| <div class=NavFrame style="CLEAR: both"> | <div class=NavFrame style="CLEAR: both"> | ||
| - | <div class=NavHead>Lösning f </div> | + | <div class=NavHead>Lösning f) </div> |
| <div class=NavContent> | <div class=NavContent> | ||
| - | Lösning till delfråga f<br \>[[Bild:1_3_6f.gif]] | + | Lösning till delfråga f) |
| + | <table width="100%" cellspacing="10px"> | ||
| + | <tr> | ||
| + | <td align="center"> | ||
| + | [[Bild:1_3_6f.gif]] | ||
| + | </td> | ||
| + | </tr> | ||
| + | </table> | ||
| </div> | </div> | ||
| </div> | </div> | ||
Versionen från 12 maj 2007 kl. 17.17
Övning 1.3:1
Beräkna
| a) | 2^3\cdot3^2 | b) | 3^5\cdot9^{-2} | c) | (-5)^3 | d) | \Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3} |
Facit
Facit till alla delfrågor
| a) | 72 | b) | 3 | c) | -125 | d) | \displaystyle \frac{27}{8} |
Lösning a)
Lösning till delfråga a)
|
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Lösning b)
Lösning till delfråga b)
|
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Lösning c)
Lösning till delfråga c)
|
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Lösning d)
Lösning till delfråga d)
|
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Övning 1.3:2
Skriv som en potens av 2
| a) | 2\cdot4\cdot8 | b) | 0{,}25 | c) | 1 |
Facit
Facit till alla delfrågor
| a) | 2^6 | b) | 2^{-2} | c) | 2^0 |
Lösning a)
Lösning till delfråga a)
|
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Lösning b)
Lösning till delfråga b)
|
|
Lösning c)
Lösning till delfråga c)
|
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Övning 1.3:3
Skriv som en potens av 3
| a) | \displaystyle \frac{1}{3} | b) | 243 | c) | 9^2 | d) | \displaystyle \frac{1}{27} | e) | \displaystyle \frac{3}{9^2} |
Facit
Facit till alla delfrågor
| a) | 3^{-1} | b) | 3^5 | c) | 3^4 | d) | 3^{-3} | e) | 3^{-3} |
Lösning a)
Lösning till delfråga a)
|
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Lösning b)
Lösning till delfråga b)
|
|
Lösning c)
Lösning till delfråga c)
|
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Lösning d)
Lösning till delfråga d)
|
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Lösning e)
Lösning till delfråga e)
|
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Övning 1.3:4
Beräkna
| a) | 2^{9}\cdot2^{-7} | b) | 3^{13}\cdot9^{-3}\cdot27^{-2} | c) | \displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6} |
| d) | 2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4} | e) | 625\cdot(5^{8}+5^{9})^{-1} | ||
Facit
Facit till alla delfrågor
| a) | 4 | b) | 3 | c) | 625 |
| d) | 16 | e) | \displaystyle \frac{1}{3750} | ||
Lösning a)
Lösning till delfråga a)
|
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Lösning b)
Lösning till delfråga b)
|
|
Lösning c)
Lösning till delfråga c)
|
|
Lösning d)
Lösning till delfråga d)
|
|
Lösning e)
Lösning till delfråga e)
|
|
Övning 1.3:5
Beräkna
| a) | 4^{1/2} | b) | 4^{-1/2} | c) | 9^{3/2} |
| d) | \left(47^{2/3} \right) ^{3} | e) | 3^{1{,}4}\cdot3^{0{,}6} | f) | \bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2} |
Facit
Facit till alla delfrågor
| a) | 2 | b) | \displaystyle \frac{1}{2} | c) | 27 |
| d) | 2209 | e) | 9 | f) | \displaystyle \frac{25}{3} |
Lösning a)
Lösning till delfråga a)
|
|
Lösning b)
Lösning till delfråga b)
|
|
Lösning c)
Lösning till delfråga c)
|
|
Lösning d)
Lösning till delfråga d)
|
|
Lösning e)
Lösning till delfråga e)
|
|
Lösning f)
Lösning till delfråga f)
|
|
Övning 1.3:6
Avgör vilket tal som är störst av
| a) | 256^{1/3}\ och \ 200^{1/3} | b) | 0{,}5^{-3}\ och \ 0{,}4^{-3} | c) | 0{,}2^5\ och \ 0{,}2^{7} |
| d) | 400^{1/3}\ och \ \bigl(5^{1/3}\bigr)^{4} | e) | 125^{1/2}\ och \ 625^{1/3} | f) | 2^{56}\ och \ 3^{40} |
Facit
Facit till alla delfrågor
| a) | 256^{1/3}>200^{1/3} | b) | 0{,}4^{-3}>0{,}5^{-3} | c) | 0{,}2^{5}>0{,}2^{7} |
| d) | \bigl(5^{1/3}\bigr)^{4}>400^{1/3} | e) | 125^{1/2}>625^{1/3} | f) | 3^{40}>2^{56} |
Lösning a)
Lösning till delfråga a)
|
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Lösning b)
Lösning till delfråga b)
|
|
Lösning c)
Lösning till delfråga c)
|
|
Lösning d)
Lösning till delfråga d)
|
|
Lösning e)
Lösning till delfråga e)
|
|
Lösning f)
Lösning till delfråga f)
|
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