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		Current revision (14:48, 22 September 2008) (edit) (undo) Tek (Talk | contribs) m
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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}}	+	{{Displayed math||<math>0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}</math>.}}
		+
		+	Another way to see this is to rewrite the two powers as
		+
		+	{{Displayed math||<math>0\textrm{.}5^{-3}=\frac{1}{0\textrm{.}5^{3}}\quad</math> and <math>\quad 0\textrm{.}4^{-3}=\frac{1}{0\textrm{.}4^3}</math>}}
		+
		+	and because <math>0\textrm{.}5^{3} > 0\textrm{.}4^{3}</math> (see exercise a), it follows that
		+
		+	{{Displayed math||<math>\frac{1}{0\textrm{.}4^{3}} > \frac{1}{0\textrm{.}5^{3}}\,</math>,}}
		+
		+	i.e. <math>0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}\,</math>.

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Current revision

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

\displaystyle 0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}.

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

\displaystyle 0\textrm{.}5^{-3}=\frac{1}{0\textrm{.}5^{3}}\quad and \displaystyle \quad 0\textrm{.}4^{-3}=\frac{1}{0\textrm{.}4^3}

and because \displaystyle 0\textrm{.}5^{3} > 0\textrm{.}4^{3} (see exercise a), it follows that

\displaystyle \frac{1}{0\textrm{.}4^{3}} > \frac{1}{0\textrm{.}5^{3}}\,,

i.e. \displaystyle 0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}\,.