Solution 1.3:6b

From Förberedande kurs i matematik 1

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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}