Lösung 1.3:4c
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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The whole expression consists of factors having a base of 5 so the power rules can be used to simplify the expression first | The whole expression consists of factors having a base of 5 so the power rules can be used to simplify the expression first | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\begin{align} |
\frac{5^{12}}{5^{-4}}\cdot \bigl( 5^{2} \bigr)^{-6} | \frac{5^{12}}{5^{-4}}\cdot \bigl( 5^{2} \bigr)^{-6} | ||
&= \frac{5^{12}}{5^{-4}}\cdot 5^{2\cdot (-6)}\\[3pt] | &= \frac{5^{12}}{5^{-4}}\cdot 5^{2\cdot (-6)}\\[3pt] | ||
Version vom 08:18, 22. Okt. 2008
The whole expression consists of factors having a base of 5 so the power rules can be used to simplify the expression first
| \displaystyle \begin{align}
\frac{5^{12}}{5^{-4}}\cdot \bigl( 5^{2} \bigr)^{-6} &= \frac{5^{12}}{5^{-4}}\cdot 5^{2\cdot (-6)}\\[3pt] &= \frac{5^{12}}{5^{-4}}\cdot 5^{-12}\\[3pt] &= \frac{5^{12}\cdot 5^{-12}}{5^{-4}}\\[3pt] &= \frac{5^{12-12}}{5^{-4}}\\[3pt] &= \frac{5^{0}}{5^{-4}}\\[3pt] &= 5^{0-(-4)}\\[3pt] &= 5^{4}\\[3pt] &= 5\cdot 5\cdot 5\cdot 5\\[3pt] &= 625\,\textrm{.} \end{align} |
