Simplify (2x^2y^(1/3))^5

${(2 x^{2} y^{\frac{1}{3}})}^{5}$

Step 1

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

Apply the product rule to $2 x^{2} y^{\frac{1}{3}}$ .

${(2 x^{2})}^{5} {(y^{\frac{1}{3}})}^{5}$

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

$2^{5} {(x^{2})}^{5} {(y^{\frac{1}{3}})}^{5}$

Step 2

Raise $2$ to the power of $5$ .

$32 {(x^{2})}^{5} {(y^{\frac{1}{3}})}^{5}$

Step 3

Multiply the exponents in ${(x^{2})}^{5}$ .

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

$32 x^{2 \cdot 5} {(y^{\frac{1}{3}})}^{5}$

Multiply $2$ by $5$ .

$32 x^{10} {(y^{\frac{1}{3}})}^{5}$

Step 4

Multiply the exponents in ${(y^{\frac{1}{3}})}^{5}$ .

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

$32 x^{10} y^{\frac{1}{3} \cdot 5}$

Combine $\frac{1}{3}$ and $5$ .

$32 x^{10} y^{\frac{5}{3}}$