Solve (x^frac{1{3}}y^frac{1{3}})^5=

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

Evaluate

$$\left(xy\right)^{\frac{5}{3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\sqrt[3]{x}\sqrt[3]{y}\right)^{5}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(\sqrt[3]{x}\right)^{5}\left(\sqrt[3]{y}\right)^{5}$$

To raise a power to another power, multiply the exponents.

$$x^{\frac{1}{3}\times 5}y^{\frac{1}{3}\times 5}$$

Multiply \frac{1}{3} times 5.

$$x^{\frac{5}{3}}y^{\frac{1}{3}\times 5}$$

Multiply \frac{1}{3} times 5.

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

Expand

$$\left(xy\right)^{\frac{5}{3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\sqrt[3]{x}\sqrt[3]{y}\right)^{5}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(\sqrt[3]{x}\right)^{5}\left(\sqrt[3]{y}\right)^{5}$$

To raise a power to another power, multiply the exponents.

$$x^{\frac{1}{3}\times 5}y^{\frac{1}{3}\times 5}$$

Multiply \frac{1}{3} times 5.

$$x^{\frac{5}{3}}y^{\frac{1}{3}\times 5}$$

Multiply \frac{1}{3} times 5.

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