1.3 Exercises

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===Övning 1.3:1===
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===Exercise 1.3:1===
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Ber&auml;kna
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Calculate
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===Övning 1.3:2===
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===Exercise 1.3:2===
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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>
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===Övning 1.3:3===
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===Exercise 1.3:3===
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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>
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===Övning 1.3:4===
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===Exercise 1.3:4===
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Ber&auml;kna
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Calculate
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===Övning 1.3:5===
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===Exercise 1.3:5===
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Ber&auml;kna
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Calculate
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===Övning 1.3:6===
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===Exercise 1.3:6===
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Avg&ouml;r vilket tal som &auml;r st&ouml;rst av
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Determine which is the larger of the two numbers in each of the following cases:
{| width="100%" cellspacing="10px"
{| width="100%" cellspacing="10px"
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|width="33%" | <math>256^{1/3}\ </math> och <math>\ 200^{1/3} </math>
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|width="33%" | <math>256^{1/3}\ </math> and <math>\ 200^{1/3} </math>
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|width="33%" | <math>0{,}5^{-3}\ </math> och <math>\ 0{,}4^{-3} </math>
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|width="33%" | <math>0{,}5^{-3}\ </math> and <math>\ 0{,}4^{-3} </math>
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|width="33%" | <math>0{,}2^5\ </math> och <math>\ 0{,}2^{7} </math>
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|width="33%" | <math>0{,}2^5\ </math> and <math>\ 0{,}2^{7} </math>
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|d)

Revision as of 11:03, 3 August 2008

       Teori          Övningar      


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}
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


Exercise 1.3:2

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

a) \displaystyle 2\cdot4\cdot8 b) \displaystyle 0{,}25 c) \displaystyle 1
Svar
Svar 1.3:2
Lösning a
Lösning 1.3:2a
Lösning b
Lösning 1.3:2b
Lösning c
Lösning 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}
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


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}
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


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{,}4}\cdot3^{0{,}6} f) \displaystyle \bigl( 125 ^{1/3} \bigr)^2\cdot \bigl( 27^{1/3} \bigr)^{-2}\cdot9^{1/2}
Svar
Svar 1.3:5
Lösning a
Lösning 1.3:5a
Lösning b
Lösning 1.3:5b
Lösning c
Lösning 1.3:5c
Lösning d
Lösning 1.3:5d
Lösning e
Lösning 1.3:5e
Lösning f
Lösning 1.3:5f


Exercise 1.3:6

Determine which is the larger of the two numbers in each of the following cases:

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