Övningar 1.3

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Versionen från 16 juli 2007 kl. 08.02 (redigera)
KTH.SE:u1zpa8nw (Diskussion | bidrag)
(Ny sida: __NOTOC__ ==&Ouml;vning 1.3:1== <div class="ovning"> Ber&auml;kna <table width="100%" cellspacing="10px"> <tr align="left"> <td class="ntext">a)</td> <td class="ntext" width="25%">$2^3\cdo...)
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Versionen från 16 juli 2007 kl. 10.41 (redigera) (ogör)
KTH.SE:u1zpa8nw (Diskussion | bidrag)

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Rad 1: Rad 1:
__NOTOC__ __NOTOC__
-==&Ouml;vning 1.3:1==+'''&Ouml;vning 1.3:1'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Ber&auml;kna Ber&auml;kna
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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>
-==&Ouml;vning 1.3:2==+'''&Ouml;vning 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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="33%">$1$</td> <td class="ntext" width="33%">$1$</td>
</tr> </tr>
Rad 35: Rad 35:
</div> </div>
-==&Ouml;vning 1.3:3==+'''&Ouml;vning 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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</td>
<td class="ntext" width="20%">$243$</td> <td class="ntext" width="20%">$243$</td>
-<td class="ntext">c)</td>+<td class="ntext">c)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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>
-==&Ouml;vning 1.3:4==+'''&Ouml;vning 1.3:4'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Ber&auml;kna Ber&auml;kna
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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>
-==&Ouml;vning 1.3:5==+'''&Ouml;vning 1.3:5'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Ber&auml;kna Ber&auml;kna
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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>
-==&Ouml;vning 1.3:6==+'''&Ouml;vning 1.3:6'''
-<div class="ovning">+<div class="ovning" style="margin-top:-20px; margin-bottom:-5px;">
Avg&ouml;r vilket tal som &auml;r st&ouml;rst av Avg&ouml;r vilket tal som &auml;r st&ouml;rst av
-<table width="100%" cellspacing="10px">+<table width="100%">
<tr align="left"> <tr align="left">
-<td class="ntext">a)</td>+<td class="ntext">a)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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)&nbsp;&nbsp;&nbsp;</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>

Versionen från 16 juli 2007 kl. 10.41

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 $\ 3^{40}$
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