From Förberedande kurs i matematik 1

Revision as of 08:21, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 1.3:1b moved to Solution 1.3:1b: Robot: moved page) ← Previous diff		Current revision (12:43, 22 September 2008) (edit) (undo) Tek (Talk | contribs) m
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-	{{NAVCONTENT_START}}	+	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.
-	<center> [[Image:1_3_1b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+	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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		+	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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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\,.