Solution 1.3:4c

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m (Lösning 1.3:4c moved to Solution 1.3:4c: Robot: moved page)
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The whole expression consists of factors having a base of
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<center> [[Image:1_3_4c.gif]] </center>
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<math>5</math>;
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so the power rules can be use to
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simplify the expression first:
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<math>\begin{align}
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& \frac{5^{12}}{5^{-4}}\centerdot \left( 5^{2} \right)^{-6}=\frac{5^{12}}{5^{-4}}\centerdot 5^{2\centerdot \left( -6 \right)}=\frac{5^{12}}{5^{-4}}\centerdot 5^{-12}=\frac{5^{12}\centerdot 5^{-12}}{5^{-4}} \\
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& \\
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& =\frac{5^{12-12}}{5^{-4}}=\frac{5^{0}}{5^{-4}}=5^{0-\left( -4 \right)}=5^{4}=5\centerdot 5\centerdot 5\centerdot 5=625 \\
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\end{align}</math>

Revision as of 11:50, 15 September 2008

The whole expression consists of factors having a base of \displaystyle 5;

so the power rules can be use to simplify the expression first:


\displaystyle \begin{align} & \frac{5^{12}}{5^{-4}}\centerdot \left( 5^{2} \right)^{-6}=\frac{5^{12}}{5^{-4}}\centerdot 5^{2\centerdot \left( -6 \right)}=\frac{5^{12}}{5^{-4}}\centerdot 5^{-12}=\frac{5^{12}\centerdot 5^{-12}}{5^{-4}} \\ & \\ & =\frac{5^{12-12}}{5^{-4}}=\frac{5^{0}}{5^{-4}}=5^{0-\left( -4 \right)}=5^{4}=5\centerdot 5\centerdot 5\centerdot 5=625 \\ \end{align}

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