Simplify the Radical Expression (x^8y^8)^(1/3)

${(x^{8} y^{8})}^{\frac{1}{3}}$

Apply the product rule to $x^{8} y^{8}$ .

${(x^{8})}^{\frac{1}{3}} {(y^{8})}^{\frac{1}{3}}$

Multiply the exponents in ${(x^{8})}^{\frac{1}{3}}$ .

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

$x^{8 (\frac{1}{3})} {(y^{8})}^{\frac{1}{3}}$

Combine $8$ and $\frac{1}{3}$ .

$x^{\frac{8}{3}} {(y^{8})}^{\frac{1}{3}}$

Multiply the exponents in ${(y^{8})}^{\frac{1}{3}}$ .

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

$x^{\frac{8}{3}} y^{8 (\frac{1}{3})}$

Combine $8$ and $\frac{1}{3}$ .

$x^{\frac{8}{3}} y^{\frac{8}{3}}$