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1.3 Exercises
From Förberedande kurs i matematik 1
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Revision as of 13:12, 10 September 2008
| Theory | Exercises |
Exercise 1.3:1
Calculate
| a) |  32 | b) | 9−2 | c) | | d) |  32 −3 |
Answer | Solution a | Solution b | Solution c | Solution d
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Exercise 1.3:2
Write each of the following as a power of
| a) | 48 | b) |  25 | c) | |
Answer | Solution a | Solution b | Solution c
Exercise 1.3:3
Write each of the following as a power of
| a) | | b) | | c) | | d) | | e) | |
Answer | Solution a | Solution b | Solution c | Solution d | Solution e
Exercise 1.3:4
Calculate
| a) | 2−7 | b) | 9−327−2 | 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
