Solve (8x^9y)^frac{1{3}}

$$( 8 x ^ { 9 } y ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$2\sqrt[3]{y}x^{3}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[3]{8x^{9}y^{1}}$$

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

$$\sqrt[3]{8}\sqrt[3]{x^{9}}\sqrt[3]{y^{1}}$$

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

$$2\sqrt[3]{x^{9}}\sqrt[3]{y^{1}}$$

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

$$2x^{9\times \frac{1}{3}}\sqrt[3]{y}$$

Multiply 9 times \frac{1}{3}.

$$2x^{3}\sqrt[3]{y}$$

Differentiate w.r.t. x

$$6\sqrt[3]{y}x^{2}$$