Lösung 1.3:6b
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
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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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- | {{ | + | |
+ | <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> | ||
+ | and | ||
+ | <math>0.4^{-3}=\frac{1}{0.4^{3}}</math> | ||
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+ | and because | ||
+ | <math>0.5^{3}>0.4^{3}</math> | ||
+ | (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. | ||
+ | <math>0.4^{-3}>0.5^{-3}</math> |
Version vom 12:52, 15. Sep. 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}