Lösung 1.3:4d
Aus Online Mathematik Brückenkurs 1
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| - | The partial expression | + | The partial expression <math>2^{2^{3}}</math> should be interpreted as 2 raised to the <math>2^{3}</math>, and because <math>2^{3}=2\cdot 2\cdot 2=8</math>, thus <math>2^{2^{3}}=2^{8}</math>. |
| - | <math>2^{2^{3}}</math> | + | |
| - | should be interpreted as | + | |
| - | <math>2</math> | + | |
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| - | <math>2^{3}</math>, | + | |
| - | + | In order to calculate the next part of the expression, <math>(-2)^{-4}</math>, it can be useful to do it a step at a time | |
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| - | In order to calculate the next part of the expression, | + | |
| - | <math> | + | |
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| - | it can be useful to do it a step at a time | + | |
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| + | {{Displayed math||<math>\begin{align} | ||
| + | (-2)^{-4} &= \frac{1}{(-2)^{4}} = \frac{1}{((-1)\cdot 2)^{4}} = \frac{1}{(-1)^{4}\cdot 2^{4}}\\[5pt] | ||
| + | &= \frac{1}{1\cdot 2^{4}} = \frac{1}{2^{4}} = 2^{-4}\,\textrm{.} | ||
| + | \end{align}</math>}} | ||
Thus, | Thus, | ||
| - | + | {{Displayed math||<math>2^{2^{3}}\cdot (-2)^{-4} = 2^{8}\cdot 2^{-4} = 2^{8-4} = 2^{4} = 16\,</math>.}} | |
| - | <math>2^{2^{3}}\ | + | |
Version vom 14:10, 22. Sep. 2008
The partial expression \displaystyle 2^{2^{3}} should be interpreted as 2 raised to the \displaystyle 2^{3}, and because \displaystyle 2^{3}=2\cdot 2\cdot 2=8, thus \displaystyle 2^{2^{3}}=2^{8}.
In order to calculate the next part of the expression, \displaystyle (-2)^{-4}, it can be useful to do it a step at a time
Thus,
