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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...)
← Gå till föregående ändring		 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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