## Intermediate Algebra for College Students (7th Edition)

$y\sqrt{xy}$
RECALL: (i) $\sqrt[n]{a} = a^{\frac{1}{n}}$ (ii) $\sqrt[n]{a^m} = a^{\frac{m}{n}}$ (iii) $(ab)^m = a^mb^m$ (iv) $(a^m)^n=a^{mn}$ The expression inside the radical sign can be written as: $=\sqrt[4]{x^2(y^3)^2} \\=\sqrt[4]{(xy^3)^2}$ Use the rules above to have: $=\left((xy^3)^2\right)^{\frac{1}{4}} \\=(xy^3)^{2\cdot\frac{1}{4}} \\=(xy^3)^{\frac{1}{2}} \\=\sqrt{xy^3} \\=\sqrt{x\cdot y^2 \cdot y} \\=y\sqrt{xy}$