## Algebra: A Combined Approach (4th Edition)

$(\frac{2x^2}{y^4})^3(\frac{2x^5}{y})^{-2}$ $= \frac{2}{x^4y^{10}}$
$(\frac{2x^2}{y^4})^3(\frac{2x^5}{y})^{-2}$ $\frac{(2x^2)^3}{(y^4)^3}\frac{(2x^5)^{-2}}{(y)^{-2}}$ (Power of a quotient) $= (\frac{2^3x^6}{y^{12}})(\frac{2^{-2}x^{-10}}{y^{-2}})$ (Power rule) $= \frac{2^{3+(-2)}x^{6+(-10)}}{y^{12+(-2)}}$ (Product rule) $= \frac{2^1x^{-4}}{y^{10}}$ $= \frac{2}{x^4y^{10}}$ (Negative exponent)