Chapter 6 Rational Exponents and Radical Functions - 6.2 Apply Properties of Rational Exponents - 6.2 Exercises - Quiz for Lessons 6.1-6.2 - Page 427: 11

$=y^{\frac{1}{2}}(x^{\frac{3}{4}}+2x^{\frac{2}{3}})$

$(x^6y^4)^{\frac{1}{8}}+2(x^{\frac{1}{3}}y^{\frac{1}{4}})^2$ $=(x^{\frac{3}{4}}y^{\frac{1}{2}})+2(x^{\frac{2}{3}}y^{\frac{1}{2}})$ $=(x^{\frac{3}{4}}y^{\frac{1}{2}})+2x^{\frac{2}{3}}y^{\frac{1}{2}}$ $=y^{\frac{1}{2}}(x^{\frac{3}{4}}y^{\frac{1}{2}}y^{\frac{-1}{2}}+2x^{\frac{2}{3}}y^{\frac{1}{2}}y^{\frac{-1}{2}})$ $=y^{\frac{1}{2}}(x^{\frac{3}{4}}y^0+2x^{\frac{2}{3}}y^0)$ $=y^{\frac{1}{2}}(x^{\frac{3}{4}}+2x^{\frac{2}{3}})$