Solve (-8m^3n^6)^1/3

$$( - 8 m ^ { 3 } n ^ { 6 } ) ^ { 1 / 3 }$$

Evaluate

$$-2mn^{2}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[3]{-8m^{3}n^{6}}$$

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

$$\sqrt[3]{-8}\sqrt[3]{m^{3}}\sqrt[3]{n^{6}}$$

Raise -8 to the power \frac{1}{3}.

$$-2\sqrt[3]{m^{3}}\sqrt[3]{n^{6}}$$

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

$$-2m^{3\times \frac{1}{3}}n^{6\times \frac{1}{3}}$$

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

$$-2mn^{6\times \frac{1}{3}}$$

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

$$-2mn^{2}$$

Differentiate w.r.t. m

$$-2n^{2}$$