Chapter 7 - Exponents and Exponential Functions - 7-5 Rational Exponents and Radicals - Practice and Problem-Solving Exercises - Page 451: 46

$3x^{\frac{1}{2}}+5y^{\frac{3}{4}}$

We are given: $(\sqrt[4] (9x)^2 + \sqrt[4]625y^3$ $=(\sqrt[4] (3^2x)^2+ \sqrt[4] 5^4y^3$ $=\sqrt[4] 3^4x^2+5\sqrt[4]y^3$ $=3\sqrt[4] x^2+5y^{\frac{3}{4}}$ $=3x^{\frac{1}{2}}+5y^{\frac{3}{4}}$