Lösung 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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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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{{Displayed math||<math>0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}</math>.}}
Another way to see this is to rewrite the two powers as
Another way to see this is to rewrite the two powers as
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{{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>}}
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<math>0.5^{-3}=\frac{1}{0.5^{3}}</math>
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and because <math>0\textrm{.}5^{3} > 0\textrm{.}4^{3}</math> (see exercise a), it follows that
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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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{{Displayed math||<math>\frac{1}{0\textrm{.}4^{3}} > \frac{1}{0\textrm{.}5^{3}}\,</math>,}}
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i.e.
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i.e. <math>0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}\,</math>.
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<math>0.4^{-3}>0.5^{-3}</math>
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Version vom 14:48, 22. Sep. 2008

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

Vorlage:Displayed math

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

Vorlage:Displayed math

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

Vorlage:Displayed math

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

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_1.3:6b“