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

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

Step 1

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

Apply the product rule to $2 x^{\frac{1}{3}} y^{\frac{3}{5}}$ .

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

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

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

Step 2

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

$4 {(x^{\frac{1}{3}})}^{2} {(y^{\frac{3}{5}})}^{2}$

Step 3

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

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

$4 x^{\frac{1}{3} \cdot 2} {(y^{\frac{3}{5}})}^{2}$

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

$4 x^{\frac{2}{3}} {(y^{\frac{3}{5}})}^{2}$

Step 4

Multiply the exponents in ${(y^{\frac{3}{5}})}^{2}$ .

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

$4 x^{\frac{2}{3}} y^{\frac{3}{5} \cdot 2}$

Multiply $\frac{3}{5} \cdot 2$ .

Combine $\frac{3}{5}$ and $2$ .

$4 x^{\frac{2}{3}} y^{\frac{3 \cdot 2}{5}}$

Multiply $3$ by $2$ .

$4 x^{\frac{2}{3}} y^{\frac{6}{5}}$