Question

The simplest form of ${\left(\frac{64}{729}\right)}^{-1/6}$is
(a) $\frac{2}{3}$
(b) $\frac{3}{2}$
(c) $\frac{4}{3}$
(d) $\frac{3}{4}$

Answer 1

(b) $\frac{3}{2}$
$$\begin{gathered} {\left(\frac{64}{729}\right)}^{\frac{-1}{6}}={\left(\frac{729}{64}\right)}^{\frac{1}{6}} \\ \mathrm{We}\mathrm{know}: \\ {2}^6=64\mathrm{and}{3}^6=729 \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ {\left(\frac{729}{64}\right)}^{\frac{1}{6}}=\frac{3^{6\times {\displaystyle \frac{1}{6}}}}{2^{6\times {\displaystyle \frac{1}{6}}}}=\frac{3}{2} \end{gathered}$$