1.3 Exercises

From Förberedande kurs i matematik 1

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{| border="0" cellspacing="0" cellpadding="0" height="30" width="100%"
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{{Not selected tab|[[1.3 Powers|Theory]]}}
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{{Selected tab|[[1.3 Exercises|Exercises]]}}
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===Övning 1.3:1===
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===Exercise 1.3:1===
<div class="ovning">
<div class="ovning">
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Ber&auml;kna
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Calculate
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="25%"| <math>\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}</math>
|width="25%"| <math>\Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.3:1|Lösning a|Lösning 1.3:1a|Lösning b|Lösning 1.3:1b|Lösning c|Lösning 1.3:1c|Lösning d|Lösning 1.3:1d}}
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</div>{{#NAVCONTENT:Answer|Answer 1.3:1|Solution a|Solution 1.3:1a|Solution b|Solution 1.3:1b|Solution c|Solution 1.3:1c|Solution d|Solution 1.3:1d}}
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===Övning 1.3:2===
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===Exercise 1.3:2===
<div class="ovning">
<div class="ovning">
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Skriv som en potens av <math>2</math>
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Write each of the following as a power of <math>2</math>
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
|width="33%"| <math>2\cdot4\cdot8</math>
|width="33%"| <math>2\cdot4\cdot8</math>
|b)
|b)
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|width="33%"| <math>0{,}25</math>
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|width="33%"| <math>0\textrm{.}25</math>
|c)
|c)
|width="33%"| <math>1</math>
|width="33%"| <math>1</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.3:2|Lösning a|Lösning 1.3:2a|Lösning b|Lösning 1.3:2b|Lösning c|Lösning 1.3:2c}}
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</div>{{#NAVCONTENT:Answer|Answer 1.3:2|Solution a|Solution 1.3:2a|Solution b|Solution 1.3:2b|Solution c|Solution 1.3:2c}}
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===Övning 1.3:3===
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===Exercise 1.3:3===
<div class="ovning">
<div class="ovning">
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Skriv som en potens av <math>3</math>
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Write each of the following as a power of <math>3</math>
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|width="20%"| <math>\displaystyle \frac{3}{9^2}</math>
|width="20%"| <math>\displaystyle \frac{3}{9^2}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.3:3|Lösning a|Lösning 1.3:3a|Lösning b|Lösning 1.3:3b|Lösning c|Lösning 1.3:3c|Lösning d|Lösning 1.3:3d|Lösning e|Lösning 1.3:3e}}
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</div>{{#NAVCONTENT:Answer|Answer 1.3:3|Solution a|Solution 1.3:3a|Solution b|Solution 1.3:3b|Solution c|Solution 1.3:3c|Solution d|Solution 1.3:3d|Solution e|Solution 1.3:3e}}
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===Övning 1.3:4===
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===Exercise 1.3:4===
<div class="ovning">
<div class="ovning">
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Ber&auml;kna
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Calculate
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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||<math>625\cdot(5^{8}+5^{9})^{-1}</math>
||<math>625\cdot(5^{8}+5^{9})^{-1}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.3:4|Lösning a|Lösning 1.3:4a|Lösning b|Lösning 1.3:4b|Lösning c|Lösning 1.3:4c|Lösning d|Lösning 1.3:4d|Lösning e|Lösning 1.3:4e}}
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</div>{{#NAVCONTENT:Answer|Answer 1.3:4|Solution a|Solution 1.3:4a|Solution b|Solution 1.3:4b|Solution c|Solution 1.3:4c|Solution d|Solution 1.3:4d|Solution e|Solution 1.3:4e}}
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===Övning 1.3:4===
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===Exercise 1.3:5===
<div class="ovning">
<div class="ovning">
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Ber&auml;kna
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Calculate
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
|a)
|a)
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|| <math>\left(47^{2/3} \right) ^{3}</math>
|| <math>\left(47^{2/3} \right) ^{3}</math>
|e)
|e)
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||<math>3^{1{,}4}\cdot3^{0{,}6}</math>
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||<math>3^{1\textrm{.}4}\cdot3^{0\textrm{.}6}</math>
|f)
|f)
||<math>\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}</math>
||<math>\bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}</math>
|}
|}
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</div>{{#NAVCONTENT:Svar|Svar 1.3:4|Lösning a|Lösning 1.3:4a|Lösning b|Lösning 1.3:4b|Lösning c|Lösning 1.3:4c|Lösning d|Lösning 1.3:4d|Lösning e|Lösning 1.3:4e|Lösning f|Lösning 1.3:4f}}
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</div>{{#NAVCONTENT:Answer|Answer 1.3:5|Solution a|Solution 1.3:5a|Solution b|Solution 1.3:5b|Solution c|Solution 1.3:5c|Solution d|Solution 1.3:5d|Solution e|Solution 1.3:5e|Solution f|Solution 1.3:5f}}
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===Exercise 1.3:6===
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<div class="ovning">
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In each of the following cases, determine which is the larger of the two numbers.
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{| width="100%" cellspacing="10px"
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|a)
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|width="33%" | <math>256^{1/3}\ </math> and <math>\ 200^{1/3} </math>
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|b)
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|width="33%" | <math>0\textrm{.}5^{-3}\ </math> and <math>\ 0\textrm{.}4^{-3} </math>
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|c)
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|width="33%" | <math>0\textrm{.}2^5\ </math> and <math>\ 0\textrm{.}2^{7} </math>
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|-
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|d)
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|| <math>400^{1/3}\ </math> and <math>\ \bigl(5^{1/3}\bigr)^{4} </math>
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|e)
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||<math>125^{1/2}\ </math> and <math>\ 625^{1/3} </math>
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|f)
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||<math>2^{56}\ </math> and <math>\ 3^{40} </math>
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|}
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</div>{{#NAVCONTENT:Answer|Answer 1.3:6|Solution a|Solution 1.3:6a|Solution b|Solution 1.3:6b|Solution c|Solution 1.3:6c|Solution d|Solution 1.3:6d|Solution e|Solution 1.3:6e|Solution f|Solution 1.3:6f}}

Current revision

       Theory          Exercises      


Exercise 1.3:1

Calculate

a) \displaystyle 2^3\cdot3^2 b) \displaystyle 3^5\cdot9^{-2} c) \displaystyle (-5)^3 d) \displaystyle \Bigl(\displaystyle \frac{2}{3}\Bigr)^{-3}
Answer
Answer 1.3:1
Solution a
Solution 1.3:1a
Solution b
Solution 1.3:1b
Solution c
Solution 1.3:1c
Solution d
Solution 1.3:1d


Exercise 1.3:2

Write each of the following as a power of \displaystyle 2

a) \displaystyle 2\cdot4\cdot8 b) \displaystyle 0\textrm{.}25 c) \displaystyle 1
Answer
Answer 1.3:2
Solution a
Solution 1.3:2a
Solution b
Solution 1.3:2b
Solution c
Solution 1.3:2c


Exercise 1.3:3

Write each of the following as a power of \displaystyle 3

a) \displaystyle \displaystyle \frac{1}{3} b) \displaystyle 243 c) \displaystyle 9^2 d) \displaystyle \displaystyle \frac{1}{27} e) \displaystyle \displaystyle \frac{3}{9^2}
Answer
Answer 1.3:3
Solution a
Solution 1.3:3a
Solution b
Solution 1.3:3b
Solution c
Solution 1.3:3c
Solution d
Solution 1.3:3d
Solution e
Solution 1.3:3e


Exercise 1.3:4

Calculate

a) \displaystyle 2^{9}\cdot2^{-7} b) \displaystyle 3^{13}\cdot9^{-3}\cdot27^{\,-2} c) \displaystyle \displaystyle \frac{5^{12}}{5^{-4}}\cdot(5^{2})^{-6}
d) \displaystyle 2^{2^{\scriptstyle3}}\cdot(-2)^{\scriptstyle-4} e) \displaystyle 625\cdot(5^{8}+5^{9})^{-1}
Answer
Answer 1.3:4
Solution a
Solution 1.3:4a
Solution b
Solution 1.3:4b
Solution c
Solution 1.3:4c
Solution d
Solution 1.3:4d
Solution e
Solution 1.3:4e


Exercise 1.3:5

Calculate

a) \displaystyle 4^{1/2} b) \displaystyle 4^{-1/2} c) \displaystyle 9^{3/2}
d) \displaystyle \left(47^{2/3} \right) ^{3} e) \displaystyle 3^{1\textrm{.}4}\cdot3^{0\textrm{.}6} f) \displaystyle \bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}
Answer
Answer 1.3:5
Solution a
Solution 1.3:5a
Solution b
Solution 1.3:5b
Solution c
Solution 1.3:5c
Solution d
Solution 1.3:5d
Solution e
Solution 1.3:5e
Solution f
Solution 1.3:5f


Exercise 1.3:6

In each of the following cases, determine which is the larger of the two numbers.

a) \displaystyle 256^{1/3}\ and \displaystyle \ 200^{1/3} b) \displaystyle 0\textrm{.}5^{-3}\ and \displaystyle \ 0\textrm{.}4^{-3} c) \displaystyle 0\textrm{.}2^5\ and \displaystyle \ 0\textrm{.}2^{7}
d) \displaystyle 400^{1/3}\ and \displaystyle \ \bigl(5^{1/3}\bigr)^{4} e) \displaystyle 125^{1/2}\ and \displaystyle \ 625^{1/3} f) \displaystyle 2^{56}\ and \displaystyle \ 3^{40}
Answer
Answer 1.3:6
Solution a
Solution 1.3:6a
Solution b
Solution 1.3:6b
Solution c
Solution 1.3:6c
Solution d
Solution 1.3:6d
Solution e
Solution 1.3:6e
Solution f
Solution 1.3:6f
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