Mathematics

The key is recognizing that a radical in the denominator is really a negative fractional exponent. Rewrite $\sqrt[5]{x^{2}y^{3}}$ as $(x^{2}y^{3})^{1/5}$, then use the power rule to distribute the exponent to each variable. Finally, move the result from denominator to numerator by flipping the sign of the exponent—this transforms division into subtraction of exponents.

The key is recognizing that a radical in the denominator is really a negative fractional exponent. Rewrite $\sqrt[5]{x^{2}y^{3}}$ as $(x^{2}y^{3})^{1/5}$, then use the power rule to distribute the exponent to each variable. Finally, move the result from denominator to numerator by flipping the sign of the exponent—this transforms division into subtraction of exponents.