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1.3 Exercises

From Förberedande kurs i matematik 1

Revision as of 13:43, 10 September 2008 by Tekbot (Talk | contribs)
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       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) 025 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) \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 | Solution a | Solution b | Solution c | Solution d | Solution e


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}

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


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}\ 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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