1.3 Exercises

From Förberedande kurs i matematik 1

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|width="33%"| <math>2\cdot4\cdot8</math>
|width="33%"| <math>2\cdot4\cdot8</math>
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|width="33%"| <math>0{,}25</math>
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|width="33%"| <math>0\textrm{.}25</math>
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|width="33%"| <math>1</math>
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|| <math>\left(47^{2/3} \right) ^{3}</math>
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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>
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||<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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===Exercise 1.3:6===
===Exercise 1.3:6===
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Determine which is the larger of the two numbers in each of the following cases:
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In each of the following cases, determine which is the larger of the two numbers.
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|width="33%" | <math>256^{1/3}\ </math> and <math>\ 200^{1/3} </math>
|width="33%" | <math>256^{1/3}\ </math> and <math>\ 200^{1/3} </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\textrm{.}5^{-3}\ </math> and <math>\ 0\textrm{.}4^{-3} </math>
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|width="33%" | <math>0{,}2^5\ </math> and <math>\ 0{,}2^{7} </math>
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|width="33%" | <math>0\textrm{.}2^5\ </math> and <math>\ 0\textrm{.}2^{7} </math>
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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}


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


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}


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}


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}


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}