QuestionSimplify. $$\left(\frac{2 y^{5}}{3 x^{2} y^{7}}\right)^{4}$$
Write your answer using only positive exponents.

Studdy Solution
Combine the results to form a single fraction:
$\frac{16 \cdot y^{20}}{81 \cdot x^{8} \cdot y^{28}}$
Simplify by dividing the powers of $y$:
$= \frac{16}{81 \cdot x^{8}} \cdot \frac{y^{20}}{y^{28}} = \frac{16}{81 \cdot x^{8}} \cdot y^{-8}$
Express $y^{-8}$ with a positive exponent:
$= \frac{16}{81 \cdot x^{8} \cdot y^{8}}$
The simplified expression is:
$\boxed{\frac{16}{81 x^{8} y^{8}}}$