Solution 1.3:4d

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m (Lösning 1.3:4d moved to Solution 1.3:4d: Robot: moved page)
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The partial expression
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<center> [[Image:1_3_4d.gif]] </center>
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<math>2^{2^{3}}</math>
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should be interpreted as
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<math>2</math>
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raised to the
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<math>2^{3}</math>,
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and because
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<math>2^{3}=2\centerdot 2\centerdot 2=8</math>, thus
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<math>2^{2^{3}}=2^{8}</math>
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In order to calculate the next part of the expression,
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<math>\left( -2 \right)^{-4}</math>,
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it can be useful to do it a step at a time:
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<math>\begin{align}
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& \left( -2 \right)^{-4}=\frac{1}{\left( -2 \right)^{4}}=\frac{1}{\left( \left( -1 \right)\centerdot 2 \right)^{4}}=\frac{1}{\left( -1 \right)^{4}\centerdot 2^{4}} \\
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& \\
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& =\frac{1}{1^{4}\centerdot 2^{4}}=\frac{1}{2^{4}}=2^{-4} \\
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\end{align}</math>
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Thus,
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<math>2^{2^{3}}\centerdot \left( -2 \right)^{-4}=2^{8}\centerdot 2^{-4}=2^{8-4}=2^{4}=16</math>

Revision as of 11:53, 15 September 2008

The partial expression \displaystyle 2^{2^{3}} should be interpreted as \displaystyle 2 raised to the \displaystyle 2^{3},

and because \displaystyle 2^{3}=2\centerdot 2\centerdot 2=8, thus \displaystyle 2^{2^{3}}=2^{8}


In order to calculate the next part of the expression, \displaystyle \left( -2 \right)^{-4},

it can be useful to do it a step at a time:


\displaystyle \begin{align} & \left( -2 \right)^{-4}=\frac{1}{\left( -2 \right)^{4}}=\frac{1}{\left( \left( -1 \right)\centerdot 2 \right)^{4}}=\frac{1}{\left( -1 \right)^{4}\centerdot 2^{4}} \\ & \\ & =\frac{1}{1^{4}\centerdot 2^{4}}=\frac{1}{2^{4}}=2^{-4} \\ \end{align}


Thus,


\displaystyle 2^{2^{3}}\centerdot \left( -2 \right)^{-4}=2^{8}\centerdot 2^{-4}=2^{8-4}=2^{4}=16

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