Lösung 1.3:1b

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Because <math>9=3\cdot 3=3^{2}</math>, we have
Because <math>9=3\cdot 3=3^{2}</math>, we have
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{{Displayed math||<math>9^{-2}=\bigl( 3^{2} \bigr)^{-2}=3^{2\cdot (-2)}=3^{-4}</math>}}
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{{Abgesetzte Formel||<math>9^{-2}=\bigl( 3^{2} \bigr)^{-2}=3^{2\cdot (-2)}=3^{-4}</math>}}
and thus
and thus
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{{Displayed math||<math>3^{5}\cdot 9^{-2}=3^{5}\cdot 3^{-4}=3^{5-4}=3^1=3\,</math>.}}
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{{Abgesetzte Formel||<math>3^{5}\cdot 9^{-2}=3^{5}\cdot 3^{-4}=3^{5-4}=3^1=3\,</math>.}}

Version vom 08:16, 22. Okt. 2008

Before we begin to calculate, it is worthwhile looking at the expression first and investigating whether it can be simplified using the power rules, so as to reduce the arithmetical work somewhat.

Because \displaystyle 9=3\cdot 3=3^{2}, we have

\displaystyle 9^{-2}=\bigl( 3^{2} \bigr)^{-2}=3^{2\cdot (-2)}=3^{-4}

and thus

\displaystyle 3^{5}\cdot 9^{-2}=3^{5}\cdot 3^{-4}=3^{5-4}=3^1=3\,.
Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_1.3:1b“