From Förberedande kurs i matematik 1

Revision as of 08:28, 9 September 2008 (edit) Tekbot (Talk | contribs) m (Lösning 1.3:6b moved to Solution 1.3:6b: Robot: moved page) ← Previous diff		Revision as of 12:52, 15 September 2008 (edit) (undo) Ian (Talk | contribs) Next diff →
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-	{{NAVCONTENT_START}}	+	When a power expression has a negative exponent, the expression's value decreases when the base increases. Thus...
-	<center> [[Image:1_3_6b.gif]] </center>	+
-	{{NAVCONTENT_STOP}}	+
		+	<math>0.4^{-3}>0.5^{-3}</math>
		+
		+
		+	Another way to see this is to rewrite the two powers as
		+
		+
		+	<math>0.5^{-3}=\frac{1}{0.5^{3}}</math>
		+	and
		+	<math>0.4^{-3}=\frac{1}{0.4^{3}}</math>
		+
		+
		+	and because
		+	<math>0.5^{3}>0.4^{3}</math>
		+	(see exercise a), it follows that
		+
		+
		+	<math>\frac{1}{0.4^{3}}>\frac{1}{0.5^{3}}</math>
		+
		+
		+	i.e.
		+	<math>0.4^{-3}>0.5^{-3}</math>

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Revision as of 12:52, 15 September 2008

When a power expression has a negative exponent, the expression's value decreases when the base increases. Thus...

\displaystyle 0.4^{-3}>0.5^{-3}

Another way to see this is to rewrite the two powers as

\displaystyle 0.5^{-3}=\frac{1}{0.5^{3}} and \displaystyle 0.4^{-3}=\frac{1}{0.4^{3}}

and because \displaystyle 0.5^{3}>0.4^{3} (see exercise a), it follows that

\displaystyle \frac{1}{0.4^{3}}>\frac{1}{0.5^{3}}

i.e. \displaystyle 0.4^{-3}>0.5^{-3}