Evaluate (x^2y^8)^(2/3)

${(x^{2} y^{8})}^{\frac{2}{3}}$

Apply the product rule to $x^{2} y^{8}$ .

${(x^{2})}^{\frac{2}{3}} {(y^{8})}^{\frac{2}{3}}$

Multiply the exponents in ${(x^{2})}^{\frac{2}{3}}$ .

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

$x^{2 (\frac{2}{3})} {(y^{8})}^{\frac{2}{3}}$

Multiply $2 (\frac{2}{3})$ .

Combine $2$ and $\frac{2}{3}$ .

$x^{\frac{2 \cdot 2}{3}} {(y^{8})}^{\frac{2}{3}}$

Multiply $2$ by $2$ .

$x^{\frac{4}{3}} {(y^{8})}^{\frac{2}{3}}$

Multiply the exponents in ${(y^{8})}^{\frac{2}{3}}$ .

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

$x^{\frac{4}{3}} y^{8 (\frac{2}{3})}$

Multiply $8 (\frac{2}{3})$ .

Combine $8$ and $\frac{2}{3}$ .

$x^{\frac{4}{3}} y^{\frac{8 \cdot 2}{3}}$

Multiply $8$ by $2$ .

$x^{\frac{4}{3}} y^{\frac{16}{3}}$