Solution 1.3:1b

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Before we begin to calculate, it is worthwhile looking at the expression first and investigating
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whether it can be simplified using the power rules, so as to reduce the arithmetical work somewhat.
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Because
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<math>9=3\centerdot 3=3^{2}</math>
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, we have
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<math>9^{-2}=\left( 3^{2} \right)^{-2}=3^{2\centerdot \left( -2 \right)}=3^{-4}</math>
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and thus
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<math>3^{5}\centerdot 9^{-2}=3^{5}\centerdot 3^{-4}=3^{5-4}=3</math>

Revision as of 11:06, 15 September 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\centerdot 3=3^{2} , we have


\displaystyle 9^{-2}=\left( 3^{2} \right)^{-2}=3^{2\centerdot \left( -2 \right)}=3^{-4}


and thus


\displaystyle 3^{5}\centerdot 9^{-2}=3^{5}\centerdot 3^{-4}=3^{5-4}=3

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