Chapter 6 Rational Exponents and Radical Functions - 6.2 Apply Properties of Rational Exponents - 6.2 Exercises - Problem Solving - Page 427: 89b

See below

The volume of a sphere is $V=\frac{4}{3}\pi r^3$. The formula for the surface area of a sphere: $S=4\pi r^2 \\=4\pi (\frac{3}{4\pi}V)^{1/3})^2\\=4\pi (\frac{3}{4\pi}V)^{2/3}\\=\frac{4\pi}{(4\pi)^{2/3}}(3V)^{2/3}\\=(4\pi)^{1/3}(3V)^{2/3}$