Solve for: (8x^4y^{2/3})^{2/3}

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

Apply exponent rule $(a\cdot b)^{n}=a^{n}b^{n}$

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

$8^{\frac{2}{3}}=4$

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

Simplify $(x^{4})^{\frac{2}{3}}:{\quad}x^{\frac{8}{3}}$

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

Simplify $(y^{\frac{2}{3}})^{\frac{2}{3}}:{\quad}y^{\frac{4}{9}}$

$=4x^{\frac{8}{3}}y^{\frac{4}{9}}$