Would someone be able to tell me how $$\bigg( \frac{5}{a^4} \bigg)^{-3}$$ gets simplified to $$\frac{a^{12}}{125}?$$
Thank you!
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1-3=-1*3 so what does this tell you? – Jack Frost Nov 09 '15 at 06:31
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Here is a dirty but quick way as a rule of thumb: we have $$ \bigg( \frac{5}{a^{4}} \bigg)^{-3} = \bigg( \frac{a^{4}}{5} \bigg)^{3} = \frac{a^{12}}{125} $$
I use "dirty" here because the number $a$ should be $\neq 0$.
Yes
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So to reverse powers, you flip the fraction? Does that work in all cases? – Spica Nov 09 '15 at 06:32
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@Spica In fact, for all $a,b \in \Bbb{R}$ such that $a,b \neq 0$ we have $$\bigg( \frac{a}{b} \bigg)^{-1} = \frac{b}{a}.$$ – Yes Nov 09 '15 at 06:34
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You have:
$$ \left(\frac{5}{a^4}\right)^{-3}=\left(\frac{5^{-3}}{a^{-12}}\right)=\left(\frac{a^{12}}{5^3}\right)=\frac{a^{12}}{125} $$
Sam Weatherhog
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