Write the Fraction in Simplest Form (x^4y^7)^(2/3)

${(x^{4} y^{7})}^{\frac{2}{3}}$

Apply the product rule to $x^{4} y^{7}$ .

${(x^{4})}^{\frac{2}{3}} {(y^{7})}^{\frac{2}{3}}$

Multiply the exponents in ${(x^{4})}^{\frac{2}{3}}$ .

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

$x^{4 (\frac{2}{3})} {(y^{7})}^{\frac{2}{3}}$

Multiply $4 (\frac{2}{3})$ .

Combine $4$ and $\frac{2}{3}$ .

$x^{\frac{4 \cdot 2}{3}} {(y^{7})}^{\frac{2}{3}}$

Multiply $4$ by $2$ .

$x^{\frac{8}{3}} {(y^{7})}^{\frac{2}{3}}$

Multiply the exponents in ${(y^{7})}^{\frac{2}{3}}$ .

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

$x^{\frac{8}{3}} y^{7 (\frac{2}{3})}$

Multiply $7 (\frac{2}{3})$ .

Combine $7$ and $\frac{2}{3}$ .

$x^{\frac{8}{3}} y^{\frac{7 \cdot 2}{3}}$

Multiply $7$ by $2$ .

$x^{\frac{8}{3}} y^{\frac{14}{3}}$