Answer
$\frac{64}{p^{9}}$
Work Step by Step
We are given the expression $(\frac{4p^{6}}{p^{9}})^{3}$.
First, we can use the power rule to simplify.
$(\frac{4p^{6}}{p^{9}})^{3}=\frac{(4p^{6})^{3}}{(p^{9})^{3}}=\frac{4^{3}p^{6\times3}}{p^{9\times3}}=\frac{64p^{18}}{p^{27}}$
Next, we can use the quotient rule.
$64\times(p^{18-27})=64p^{-9}=\frac{64}{p^{9}}$
