1.3 Übungen
Aus Online Mathematik Brückenkurs 1
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| - | === | + | ===Exercise 1.3:1=== |
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| - | + | Calculate | |
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|a) | |a) | ||
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| - | === | + | ===Exercise 1.3:2=== |
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| - | + | Write each of the following as a power of <math>2</math> | |
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|a) | |a) | ||
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| - | === | + | ===Exercise 1.3:3=== |
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| - | + | Write each of the following as a power of <math>3</math> | |
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|a) | |a) | ||
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| - | === | + | ===Exercise 1.3:4=== |
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| - | + | Calculate | |
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|a) | |a) | ||
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| - | === | + | ===Exercise 1.3:5=== |
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| - | + | Calculate | |
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|a) | |a) | ||
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| - | === | + | ===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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|a) | |a) | ||
| - | |width="33%" | <math>256^{1/3}\ </math> | + | |width="33%" | <math>256^{1/3}\ </math> and <math>\ 200^{1/3} </math> |
|b) | |b) | ||
| - | |width="33%" | <math>0{,}5^{-3}\ </math> | + | |width="33%" | <math>0{,}5^{-3}\ </math> and <math>\ 0{,}4^{-3} </math> |
|c) | |c) | ||
| - | |width="33%" | <math>0{,}2^5\ </math> | + | |width="33%" | <math>0{,}2^5\ </math> and <math>\ 0{,}2^{7} </math> |
|- | |- | ||
|d) | |d) | ||
Version vom 11:03, 3. Aug. 2008
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} |
Svar
Laden...
Lösning a
Lösning b
Lösning c
Lösning d
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 |
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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning 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} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning 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}\ och \displaystyle \ \bigl(5^{1/3}\bigr)^{4} | e) | \displaystyle 125^{1/2}\ och \displaystyle \ 625^{1/3} | f) | \displaystyle 2^{56}\ och \displaystyle \ 3^{40} |
Svar
Lösning a
Lösning b
Lösning c
Lösning d
Lösning e
Lösning f
