Lösung 1.3:4d

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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
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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{{Displayed math||<math>\begin{align}
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{{Abgesetzte Formel||<math>\begin{align}
(-2)^{-4} &= \frac{1}{(-2)^{4}} = \frac{1}{((-1)\cdot 2)^{4}} = \frac{1}{(-1)^{4}\cdot 2^{4}}\\[5pt]
(-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{.}
&= \frac{1}{1\cdot 2^{4}} = \frac{1}{2^{4}} = 2^{-4}\,\textrm{.}
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Thus,
Thus,
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{{Displayed math||<math>2^{2^{3}}\cdot (-2)^{-4} = 2^{8}\cdot 2^{-4} = 2^{8-4} = 2^{4} = 16\,</math>.}}
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{{Abgesetzte Formel||<math>2^{2^{3}}\cdot (-2)^{-4} = 2^{8}\cdot 2^{-4} = 2^{8-4} = 2^{4} = 16\,</math>.}}

Version vom 08:18, 22. Okt. 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

\displaystyle \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}

Thus,

\displaystyle 2^{2^{3}}\cdot (-2)^{-4} = 2^{8}\cdot 2^{-4} = 2^{8-4} = 2^{4} = 16\,.
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_1.3:4d“