Answer
The answer is $\frac{x^9}{8y^{15}}$.
Work Step by Step
The given expression is
$\left ( \frac{2x^4y^{-2}}{4xy^3} \right )^3$.
$\left ( \frac{2x^4y^{-2}}{2^2xy^3} \right )^3$.
Subtract the exponents when dividing as shown below.
$\left ( 2^{1-2}x^{4-1}y^{-2-3} \right )^3$.
Simplify.
$\left ( 2^{-1}x^{3}y^{-5} \right )^3$.
Multiply each factor in the parentheses by $3$.
$2^{-3}x^{9}y^{-15} $.
Use $ b^{-n}=\frac{1}{b^n} $.
$\frac{x^9}{2^3y^{15}}$
Simplify.
$\frac{x^9}{8y^{15}}$.
