Answer
$(2x^{2}y)^{\frac{1}{3}}=2^{\frac{1}{3}}x^{\frac{2}{3}}y^{\frac{1}{3}}$
Work Step by Step
Step 1: The index of the radical is 3, so the denominator of the fractional exponent is 3.
Step 2: Therefore, the expression is written as $(2x^{2}y)^{\frac{1}{3}}$.
Step 3: $(2x^{2}y)^{\frac{1}{3}}=2^{\frac{1}{3}}x^{\frac{2}{3}}y^{\frac{1}{3}}$