Solution 1.3:6b

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When a power expression has a negative exponent, the expression's value decreases when the base increases. Thus...
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<center> [[Image:1_3_6b.gif]] </center>
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<math>0.4^{-3}>0.5^{-3}</math>
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Another way to see this is to rewrite the two powers as
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<math>0.5^{-3}=\frac{1}{0.5^{3}}</math>
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and
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<math>0.4^{-3}=\frac{1}{0.4^{3}}</math>
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and because
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<math>0.5^{3}>0.4^{3}</math>
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(see exercise a), it follows that
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<math>\frac{1}{0.4^{3}}>\frac{1}{0.5^{3}}</math>
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i.e.
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<math>0.4^{-3}>0.5^{-3}</math>

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}

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