Simplify (8xy^3)^(2/3)

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $8 x y^{3}$ .

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

Apply the product rule to $8 x$ .

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

Simplify the expression.

Rewrite $8$ as $2^{3}$ .

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

Raise $2$ to the power of $2$ .

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Reorder factors in $4 x^{\frac{2}{3}} y^{2}$ .

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