Simplify the Radical Expression (x^2y^5)^(1/5)

${(x^{2} y^{5})}^{\frac{1}{5}}$

Apply the product rule to $x^{2} y^{5}$ .

${(x^{2})}^{\frac{1}{5}} {(y^{5})}^{\frac{1}{5}}$

Multiply the exponents in ${(x^{2})}^{\frac{1}{5}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{2 (\frac{1}{5})} {(y^{5})}^{\frac{1}{5}}$

Combine $2$ and $\frac{1}{5}$ .

$x^{\frac{2}{5}} {(y^{5})}^{\frac{1}{5}}$

Multiply the exponents in ${(y^{5})}^{\frac{1}{5}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{2}{5}} y^{5 (\frac{1}{5})}$

Cancel the common factor of $5$ .

Cancel the common factor.

$x^{\frac{2}{5}} y^{5 (\frac{1}{5})}$

Rewrite the expression.

$x^{\frac{2}{5}} y^{1}$

Simplify.

$x^{\frac{2}{5}} y$

Reorder factors in $x^{\frac{2}{5}} y$ .

$y x^{\frac{2}{5}}$