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