Solve (125a^3b^6)^1/3

$$( 125 a ^ { 3 } b ^ { 6 } ) ^ { 1 / 3 }$$

Evaluate

$$5ab^{2}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[3]{125a^{3}b^{6}}$$

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

$$\sqrt[3]{125}\sqrt[3]{a^{3}}\sqrt[3]{b^{6}}$$

Raise 125 to the power \frac{1}{3}.

$$5\sqrt[3]{a^{3}}\sqrt[3]{b^{6}}$$

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

$$5a^{3\times \frac{1}{3}}b^{6\times \frac{1}{3}}$$

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

$$5ab^{6\times \frac{1}{3}}$$

Multiply 6 times \frac{1}{3}.

$$5ab^{2}$$

Differentiate w.r.t. a

$$5b^{2}$$