1.3 Übungen

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Version vom 13:12, 10. Sep. 2008

 

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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}
Answer
Answer 1.3:1
Solution a
Solution 1.3:1a
Solution b
Solution 1.3:1b
Solution c
Solution 1.3:1c
Solution d
Solution 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
Answer
Answer 1.3:2
Solution a
Solution 1.3:2a
Solution b
Solution 1.3:2b
Solution c
Solution 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}
Answer
Answer 1.3:3
Solution a
Solution 1.3:3a
Solution b
Solution 1.3:3b
Solution c
Solution 1.3:3c
Solution d
Solution 1.3:3d
Solution e
Solution 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}
Answer
Answer 1.3:4
Solution a
Solution 1.3:4a
Solution b
Solution 1.3:4b
Solution c
Solution 1.3:4c
Solution d
Solution 1.3:4d
Solution e
Solution 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}
Answer
Answer 1.3:5
Solution a
Solution 1.3:5a
Solution b
Solution 1.3:5b
Solution c
Solution 1.3:5c
Solution d
Solution 1.3:5d
Solution e
Solution 1.3:5e
Solution f
Solution 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}\ 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
Answer 1.3:6
Solution a
Solution 1.3:6a
Solution b
Solution 1.3:6b
Solution c
Solution 1.3:6c
Solution d
Solution 1.3:6d
Solution e
Solution 1.3:6e
Solution f
Solution 1.3:6f
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