Answer
$\displaystyle \frac{4}{3}$
Work Step by Step
$[\displaystyle \frac{27}{64}]^{-1/3}=$ ...use: $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$
$=\displaystyle \frac{27^{-1/3}}{64^{-1/3}}=$ ... recognize $64=4^{3}, 27=3^{3}$
$=\displaystyle \frac{(3^{3})^{-1/3}}{(4^{3})^{-1/3}}=$ ...use: $(a^{m})^{n}=a^{mn}$
$=\displaystyle \frac{3^{-1}}{4^{-1}}=$ ...use: $\displaystyle \frac{1}{a^{n}}=a^{-n}$
$=\displaystyle \frac{4}{3}$
