How do you simplify ${(- 343)}^{- \frac{8}{3}}$ $(-343)^(-8/3)$ ?

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Answer 1 · 2015-04-22T13:43:39

${(- 343)}^{- \frac{8}{3}}$ $(-343)^(-8/3)$

Note that $\sqrt[3]{343} = 7$ $root(3)(343)=7$

${(- 343)}^{- \frac{8}{3}}$ $(-343)^(-8/3)$

$= \frac{1}{{(- 343)}^{\frac{8}{3}}}$ $=1/((-343)^(8/3))$

$= \frac{1}{{(\sqrt[3]{- 343})}^{8}}$ $=1/((root(3)(-343))^8$

$= \frac{1}{{(- 7)}^{8}}$ $=1/(-7)^8$

$= \frac{1}{5764801}$ $=1/5764801$ (I did not multiply this out by hand)

How do you simplify (-343)^(-8/3)(−343)−83(-343)^(-8/3)?