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1.3 Exercises

From Förberedande kurs i matematik 1

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{{Ej vald flik|[[1.3 Potenser|Theory]]}}
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{{Vald flik|[[1.3 Exercises|Exercises]]}}
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|width="33%"| <math>2\cdot4\cdot8</math>
|width="33%"| <math>2\cdot4\cdot8</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>
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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) 2332 b) 359−2 c) (−5)3 d) 32−3 

Answer | Solution a | Solution b | Solution c | Solution d


Exercise 1.3:2

Write each of the following as a power of 2

a) 248 b) 0.25 c) 1

Answer | Solution a | Solution b | Solution c


Exercise 1.3:3

Write each of the following as a power of 3

a) 31 b) 243 c) 92 d) 127 e) 392

Answer | Solution a | Solution b | Solution c | Solution d | Solution e


Exercise 1.3:4

Calculate

a) 292−7 b) 3139−327−2 c) 5125−4(52)−6
d) 223(−2)−4 e) 625(58+59)−1

Answer | Solution a | Solution b | Solution c | Solution d | Solution e


Exercise 1.3:5

Calculate

a) 412  b) 4−12  c) 932 
d) 47233  e) 31.430.6 f) 1251322713−2912 

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f


Exercise 1.3:6

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

a) 25613   and  20013  b) 0.5−3  and  0.4−3 c) 0.25  and  0.27
d) 40013   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 | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

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