Write in Exponential Form ( cube root of x^2y^3z^4)^2

${(\sqrt[3]{x^{2} y^{3} z^{4}})}^{2}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2} y^{3} z^{4}}$ as ${(x^{2} y^{3} z^{4})}^{\frac{1}{3}}$ .

${({(x^{2} y^{3} z^{4})}^{\frac{1}{3}})}^{2}$

Step 2

Multiply the exponents in ${({(x^{2} y^{3} z^{4})}^{\frac{1}{3}})}^{2}$ .

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

${(x^{2} y^{3} z^{4})}^{\frac{1}{3} \cdot 2}$

Combine $\frac{1}{3}$ and $2$ .

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