Lösung 1.3:6b
Aus Online Mathematik Brückenkurs 1
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When a power expression has a negative exponent, the expression's value decreases when the base increases. Thus | When a power expression has a negative exponent, the expression's value decreases when the base increases. Thus | ||
| - | {{ | + | {{Abgesetzte Formel||<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 | ||
| - | {{ | + | {{Abgesetzte Formel||<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 | and because <math>0\textrm{.}5^{3} > 0\textrm{.}4^{3}</math> (see exercise a), it follows that | ||
| - | {{ | + | {{Abgesetzte Formel||<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>. | i.e. <math>0\textrm{.}4^{-3} > 0\textrm{.}5^{-3}\,</math>. | ||
Version vom 08:19, 22. Okt. 2008
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}\,.
