Solution 1.3:1b

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Current revision (12:43, 22 September 2008) (edit) (undo)
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Before we begin to calculate, it is worthwhile looking at the expression first and investigating
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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.
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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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Because <math>9=3\cdot 3=3^{2}</math>, we have
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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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{{Displayed math||<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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<math>3^{5}\centerdot 9^{-2}=3^{5}\centerdot 3^{-4}=3^{5-4}=3</math>
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Current revision

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\,.
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