Övn 1.3
Sommarmatte 1
(Skillnad mellan versioner)
| Versionen från 16 juli 2007 kl. 07.48 (redigera) KTH.SE:u1zpa8nw (Diskussion | bidrag) (Ny sida: __NOTOC__ ==Övning 1.3:1== <div class="ovning"> Beräkna <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="25%">$2^3\cd...) ← Gå till föregående ändring |
Nuvarande version (16 juli 2007 kl. 08.01) (redigera) (ogör) KTH.SE:u1zpa8nw (Diskussion | bidrag) (Tar bort sidans innehåll) |
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| - | __NOTOC__ | ||
| - | ==Övning 1.3:1== | ||
| - | <div class="ovning"> | ||
| - | Beräkna | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="25%">$2^3\cdot3^2$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="25%">$3^5\cdot9^{-2}$</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="25%">$(-5)^3$</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="25%">$\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.3:2== | ||
| - | |||
| - | <div class="ovning"> | ||
| - | Skriv som en potens av 2 | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">$2\cdot4\cdot8$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">$0{,}25$</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">$1$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.3:3== | ||
| - | |||
| - | <div class="ovning"> | ||
| - | Skriv som en potens av 3 | ||
| - | <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> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.3:4== | ||
| - | |||
| - | <div class="ovning"> | ||
| - | Beräkna | ||
| - | <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" width="33%">$2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}$</td> | ||
| - | <td class="ntext">e)</td> | ||
| - | <td class="ntext" width="33%">$625\cdot(5^{8}+5^{9})^{-1}$</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 1.3:5== | ||
| - | |||
| - | <div class="ovning"> | ||
| - | Beräkna | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">$4^{1/2}$</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">$4^{-1/2}$</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">$9^{3/2}$</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="33%">$\left(47^{2/3} \right) ^{3}$</td> | ||
| - | <td class="ntext">e)</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> | ||
| - | |||
| - | ==Övning 1.3:6== | ||
| - | <div class="ovning"> | ||
| - | Avgör vilket tal som är störst 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> | ||
