Solve (a^2b^2)^frac{1{3}}

$$( a ^ { 2 } b ^ { 2 } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$\left(ab\right)^{\frac{2}{3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[3]{a^{2}b^{2}}$$

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

$$\sqrt[3]{a^{2}}\sqrt[3]{b^{2}}$$

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

$$a^{2\times \frac{1}{3}}b^{2\times \frac{1}{3}}$$

Multiply 2 times \frac{1}{3}.

$$a^{\frac{2}{3}}b^{2\times \frac{1}{3}}$$

Multiply 2 times \frac{1}{3}.

$$a^{\frac{2}{3}}b^{\frac{2}{3}}$$

Differentiate w.r.t. a

$$\frac{2b^{\frac{2}{3}}}{3\sqrt[3]{a}}$$