1.3 Övningar

Sommarmatte 1

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Versionen från 28 april 2007 kl. 13.13 (redigera)
Ossiang (Diskussion | bidrag)
(Övning 1.3:3)
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Nuvarande version (25 maj 2007 kl. 11.14) (redigera) (ogör)
KTH.SE:u1qh5fat (Diskussion | bidrag)
(Övning 1.3:4)
 
(11 mellanliggande versioner visas inte.)
Rad 4: Rad 4:
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 21:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</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 39:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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 99:
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 114:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</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 130:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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 176:
Skriv som en potens av 3 Skriv som en potens av 3
<table width="100%" cellspacing="10px"> <table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="20%">$\displaystyle \frac{1}{3}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="20%">$243$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="20%">$9^2$</td>
 +<td class="ntext">d)</td>
 +<td class="ntext" width="20%">$\displaystyle \frac{1}{27}$</td>
 +<td class="ntext">e)</td>
 +<td class="ntext" width="20%">$\displaystyle \frac{3}{9^2}$</td>
 +</tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
 +</table>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor<br \>
 +<table width="100%" cellspacing="10px">
<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%">$3^{-1}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$243$</td>+<td class="ntext" width="20%">$3^5$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$9^2$</td>+<td class="ntext" width="20%">$3^4$</td>
 +<td class="ntext">d)</td>
 +<td class="ntext" width="20%">$3^{-3}$</td>
 +<td class="ntext">e)</td>
 +<td class="ntext" width="20%">$3^{-3}$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_3a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_3b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_3c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_3d.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning e)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga e)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_3e.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +==&Ouml;vning 1.3:4==
 + 
 +<div class="ovning">
 +Ber&auml;kna
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="33%">$2^{9}\cdot2^{-7}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="33%">$3^{13}\cdot9^{-3}\cdot27^{\,-2}$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$\displaystyle \frac{1}{27}$</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">$\displaystyle \frac{3}{9^2}$</td>+<td class="ntext" width="33%">$625\cdot(5^{8}+5^{9})^{-1}$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 151: Rad 310:
<div class=NavHead>Facit&nbsp;</div> <div class=NavHead>Facit&nbsp;</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 align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="33%">$4$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="33%">$3$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$625$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)</td>
 +<td class="ntext" width="33%">$16$</td>
 +<td class="ntext">e)</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{1}{3750}$</td>
 +</tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_4a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_4b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_4c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_4d.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning e)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga e)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_4e.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 +
 +==&Ouml;vning 1.3:5==
 +
 +<div class="ovning">
 +Ber&auml;kna
 +<table width="100%" cellspacing="10px">
<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="33%">$4^{1/2}$</td>
<td class="ntext">b)</td> <td class="ntext">b)</td>
-<td class="ntext">$3^5$</td>+<td class="ntext" width="33%">$4^{-1/2}$</td>
<td class="ntext">c)</td> <td class="ntext">c)</td>
-<td class="ntext">$3^4$</td>+<td class="ntext" width="33%">$9^{3/2}$</td>
 +</tr>
 +<tr align="left">
<td class="ntext">d)</td> <td class="ntext">d)</td>
-<td class="ntext">$3^{-3}$</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">$3^{-3}$</td>+<td class="ntext" width="33%">$3^{1{,}4}\cdot3^{0{,}6}$</td>
 +<td class="ntext">f)</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><td height="5px"/></tr>
 +</table>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor<br \>
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="33%">$2$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{1}{2}$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$27$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)</td>
 +<td class="ntext" width="33%">$2209$</td>
 +<td class="ntext">e)</td>
 +<td class="ntext" width="33%">$9$</td>
 +<td class="ntext">f)</td>
 +<td class="ntext" width="33%">$\displaystyle \frac{25}{3}$</td>
</tr> </tr>
<tr><td height="5px"/></tr> <tr><td height="5px"/></tr>
Rad 172: Rad 453:
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning a&nbsp;</div>+<div class=NavHead>L&ouml;sning a)&nbsp;</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_5a.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning b&nbsp;</div>+<div class=NavHead>L&ouml;sning b)&nbsp;</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_5b.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning c&nbsp;</div>+<div class=NavHead>L&ouml;sning c)&nbsp;</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_5c.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning d&nbsp;</div>+<div class=NavHead>L&ouml;sning d)&nbsp;</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_5d.gif]]
 +</td>
 +</tr>
 +</table>
</div> </div>
</div> </div>
<div class=NavFrame style="CLEAR: both"> <div class=NavFrame style="CLEAR: both">
-<div class=NavHead>L&ouml;sning e&nbsp;</div>+<div class=NavHead>L&ouml;sning e)&nbsp;</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_5e.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning f)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga f)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_5f.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +==&Ouml;vning 1.3:6==
 +<div class="ovning">
 +Avg&ouml;r vilket tal som &auml;r st&ouml;rst av
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="33%">$256^{1/3}\ $ och $\ 200^{1/3}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="33%">$0{,}5^{-3}\ $ och $\ 0{,}4^{-3}$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$0{,}2^5\ $ och $\ 0{,}2^{7}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)</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" width="33%">$125^{1/2}\ $ och $\ 625^{1/3}$</td>
 +<td class="ntext">f)</td>
 +<td class="ntext" width="33%">$2^{56}\ $ och $\ 3^{40}$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>Facit&nbsp;</div>
 +<div class=NavContent>
 +Facit till alla delfrågor<br \>
 +<table width="100%" cellspacing="10px">
 +<tr align="left">
 +<td class="ntext">a)</td>
 +<td class="ntext" width="33%">$256^{1/3}>200^{1/3}$</td>
 +<td class="ntext">b)</td>
 +<td class="ntext" width="33%">$0{,}4^{-3}>0{,}5^{-3}$</td>
 +<td class="ntext">c)</td>
 +<td class="ntext" width="33%">$0{,}2^{5}>0{,}2^{7}$</td>
 +</tr>
 +<tr align="left">
 +<td class="ntext">d)</td>
 +<td class="ntext" width="33%">$\bigl(5^{1/3}\bigr)^{4}>400^{1/3}$</td>
 +<td class="ntext">e)</td>
 +<td class="ntext" width="33%">$125^{1/2}>625^{1/3}$</td>
 +<td class="ntext">f)</td>
 +<td class="ntext" width="33%">$3^{40}>2^{56}$</td>
 +</tr>
 +<tr><td height="5px"/></tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning a)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga a)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_6a.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning b)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga b)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_6b.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning c)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga c)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_6c.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning d)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga d)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_6d.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning e)&nbsp;</div>
 +<div class=NavContent>
 +Lösning till delfråga e)
 +<table width="100%" cellspacing="10px">
 +<tr>
 +<td align="center">
 +[[Bild:1_3_6e.gif]]
 +</td>
 +</tr>
 +</table>
 +</div>
 +</div>
 + 
 +<div class=NavFrame style="CLEAR: both">
 +<div class=NavHead>L&ouml;sning f)&nbsp;</div>
 +<div class=NavContent>
 +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>

Nuvarande version

Innehåll

[redigera] Övning 1.3:1

Beräkna

a) $2^3\cdot3^2$ b) $3^5\cdot9^{-2}$ c) $(-5)^3$ d) $\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$

[redigera] Övning 1.3:2

Skriv som en potens av 2

a) $2\cdot4\cdot8$ b) $0{,}25$ c) $1$

[redigera] 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) $\displaystyle \frac{3}{9^2}$

[redigera] 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) $625\cdot(5^{8}+5^{9})^{-1}$

[redigera] 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) $\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$

[redigera] 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 $\ 3^{40}$
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