Övningar 1.3
Sommarmatte 1
(Skillnad mellan versioner)
| Versionen från 16 juli 2007 kl. 08.02 (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\cdo...) ← Gå till föregående ändring |
Nuvarande version (17 juli 2007 kl. 09.37) (redigera) (ogör) KTH.SE:u1zpa8nw (Diskussion | bidrag) |
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| (En mellanliggande version visas inte.) | |||
| Rad 1: | Rad 1: | ||
| __NOTOC__ | __NOTOC__ | ||
| - | ==Övning 1.3:1== | + | '''Övning 1.3:1''' |
| - | <div class="ovning"> | + | <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> |
| Beräkna | Beräkna | ||
| - | <table width="100%" cellspacing="10px"> | + | <table width="100%"> |
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | + | <td class="ntext">a) </td> |
| <td class="ntext" width="25%">$2^3\cdot3^2$</td> | <td class="ntext" width="25%">$2^3\cdot3^2$</td> | ||
| - | <td class="ntext">b)</td> | + | <td class="ntext">b) </td> |
| <td class="ntext" width="25%">$3^5\cdot9^{-2}$</td> | <td class="ntext" width="25%">$3^5\cdot9^{-2}$</td> | ||
| - | <td class="ntext">c)</td> | + | <td class="ntext">c) </td> |
| <td class="ntext" width="25%">$(-5)^3$</td> | <td class="ntext" width="25%">$(-5)^3$</td> | ||
| - | <td class="ntext">d)</td> | + | <td class="ntext">d) </td> |
| <td class="ntext" width="25%">$\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$</td> | <td class="ntext" width="25%">$\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$</td> | ||
| </tr> | </tr> | ||
| Rad 18: | Rad 18: | ||
| </div> | </div> | ||
| - | ==Övning 1.3:2== | + | '''Övning 1.3:2''' |
| - | <div class="ovning"> | + | <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> |
| Skriv som en potens av 2 | Skriv som en potens av 2 | ||
| - | <table width="100%" cellspacing="10px"> | + | <table width="100%"> |
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | + | <td class="ntext">a) </td> |
| <td class="ntext" width="33%">$2\cdot4\cdot8$</td> | <td class="ntext" width="33%">$2\cdot4\cdot8$</td> | ||
| - | <td class="ntext">b)</td> | + | <td class="ntext">b) </td> |
| <td class="ntext" width="33%">$0{,}25$</td> | <td class="ntext" width="33%">$0{,}25$</td> | ||
| - | <td class="ntext">c)</td> | + | <td class="ntext">c) </td> |
| <td class="ntext" width="33%">$1$</td> | <td class="ntext" width="33%">$1$</td> | ||
| </tr> | </tr> | ||
| Rad 35: | Rad 35: | ||
| </div> | </div> | ||
| - | ==Övning 1.3:3== | + | '''Övning 1.3:3''' |
| - | <div class="ovning"> | + | <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> |
| Skriv som en potens av 3 | Skriv som en potens av 3 | ||
| - | <table width="100%" cellspacing="10px"> | + | <table width="100%"> |
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | + | <td class="ntext">a) </td> |
| <td class="ntext" width="20%">$\displaystyle \frac{1}{3}$</td> | <td class="ntext" width="20%">$\displaystyle \frac{1}{3}$</td> | ||
| - | <td class="ntext">b)</td> | + | <td class="ntext">b) </td> |
| <td class="ntext" width="20%">$243$</td> | <td class="ntext" width="20%">$243$</td> | ||
| - | <td class="ntext">c)</td> | + | <td class="ntext">c) </td> |
| <td class="ntext" width="20%">$9^2$</td> | <td class="ntext" width="20%">$9^2$</td> | ||
| - | <td class="ntext">d)</td> | + | <td class="ntext">d) </td> |
| <td class="ntext" width="20%">$\displaystyle \frac{1}{27}$</td> | <td class="ntext" width="20%">$\displaystyle \frac{1}{27}$</td> | ||
| - | <td class="ntext">e)</td> | + | <td class="ntext">e) </td> |
| <td class="ntext" width="20%">$\displaystyle \frac{3}{9^2}$</td> | <td class="ntext" width="20%">$\displaystyle \frac{3}{9^2}$</td> | ||
| </tr> | </tr> | ||
| Rad 56: | Rad 56: | ||
| </div> | </div> | ||
| - | ==Övning 1.3:4== | + | '''Övning 1.3:4''' |
| - | <div class="ovning"> | + | <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> |
| Beräkna | Beräkna | ||
| - | <table width="100%" cellspacing="10px"> | + | <table width="100%"> |
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | + | <td class="ntext">a) </td> |
| <td class="ntext" width="33%">$2^{9}\cdot2^{-7}$</td> | <td class="ntext" width="33%">$2^{9}\cdot2^{-7}$</td> | ||
| - | <td class="ntext">b)</td> | + | <td class="ntext">b) </td> |
| <td class="ntext" width="33%">$3^{13}\cdot9^{-3}\cdot27^{\,-2}$</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" width="33%">$\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}$</td> | <td class="ntext" width="33%">$\displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}$</td> | ||
| </tr> | </tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | + | <td class="ntext">d) </td> |
| <td class="ntext" width="33%">$2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4}$</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" width="33%">$625\cdot(5^{8}+5^{9})^{-1}$</td> | <td class="ntext" width="33%">$625\cdot(5^{8}+5^{9})^{-1}$</td> | ||
| </tr> | </tr> | ||
| Rad 79: | Rad 79: | ||
| </div> | </div> | ||
| - | ==Övning 1.3:5== | + | '''Övning 1.3:5''' |
| - | <div class="ovning"> | + | <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> |
| Beräkna | Beräkna | ||
| - | <table width="100%" cellspacing="10px"> | + | <table width="100%"> |
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | + | <td class="ntext">a) </td> |
| <td class="ntext" width="33%">$4^{1/2}$</td> | <td class="ntext" width="33%">$4^{1/2}$</td> | ||
| - | <td class="ntext">b)</td> | + | <td class="ntext">b) </td> |
| <td class="ntext" width="33%">$4^{-1/2}$</td> | <td class="ntext" width="33%">$4^{-1/2}$</td> | ||
| - | <td class="ntext">c)</td> | + | <td class="ntext">c) </td> |
| <td class="ntext" width="33%">$9^{3/2}$</td> | <td class="ntext" width="33%">$9^{3/2}$</td> | ||
| </tr> | </tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | + | <td class="ntext">d) </td> |
| <td class="ntext" width="33%">$\left(47^{2/3} \right) ^{3}$</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" width="33%">$3^{1{,}4}\cdot3^{0{,}6}$</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" width="33%">$\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$</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> | ||
| Rad 104: | Rad 104: | ||
| </div> | </div> | ||
| - | ==Övning 1.3:6== | + | '''Övning 1.3:6''' |
| - | <div class="ovning"> | + | <div class="ovning" style="margin-top:-20px; margin-bottom:-5px;"> |
| Avgör vilket tal som är störst av | Avgör vilket tal som är störst av | ||
| - | <table width="100%" cellspacing="10px"> | + | <table width="100%"> |
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | + | <td class="ntext">a) </td> |
| <td class="ntext" width="33%">$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" width="33%">$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" width="33%">$0{,}2^5\ $ och $\ 0{,}2^{7}$</td> | <td class="ntext" width="33%">$0{,}2^5\ $ och $\ 0{,}2^{7}$</td> | ||
| </tr> | </tr> | ||
| <tr align="left"> | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | + | <td class="ntext">d) </td> |
| <td class="ntext" width="33%">$400^{1/3}\ $ och $\ \bigl(5^{1/3}\bigr)^{4}$</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" width="33%">$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" width="33%">$2^{56}\ $ och $\ 3^{40}$</td> | <td class="ntext" width="33%">$2^{56}\ $ och $\ 3^{40}$</td> | ||
| </tr> | </tr> | ||
| Rad 127: | Rad 127: | ||
| </table> | </table> | ||
| </div> | </div> | ||
| + | <br><br><br><br><br><br><br><br><br><br><br><br><br><br> | ||
Nuvarande version
Övning 1.3:1
Beräkna
| a) | $2^3\cdot3^2$ | b) | $3^5\cdot9^{-2}$ | c) | $(-5)^3$ | d) | $\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}$ |
Övning 1.3:2
Skriv som en potens av 2
| a) | $2\cdot4\cdot8$ | b) | $0{,}25$ | c) | $1$ |
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) | $\displaystyle \frac{3}{9^2}$ |
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) | $625\cdot(5^{8}+5^{9})^{-1}$ | ||
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) | $\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}$ |
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 $\ 3^{40}$ |
