From Förberedande kurs i matematik 1

Revision as of 06:27, 21 August 2008 (edit) Tekbot (Talk | contribs) m (Robot: Automated text replacement (-[[Bild: +[[Image:)) ← Previous diff		Current revision (12:43, 22 September 2008) (edit) (undo) Tek (Talk | contribs) m
(2 intermediate revisions not shown.)
Line 1:		Line 1:
-	{{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
		+
		+	{{Displayed math||<math>9^{-2}=\bigl( 3^{2} \bigr)^{-2}=3^{2\cdot (-2)}=3^{-4}</math>}}
		+
		+	and thus
		+
		+	{{Displayed math||<math>3^{5}\cdot 9^{-2}=3^{5}\cdot 3^{-4}=3^{5-4}=3^1=3\,</math>.}}

---

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\,.