Solve (216x^9y^12)^frac{1{3}}

$$( 216 x ^ { 9 } y ^ { 12 } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$6x^{3}y^{4}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\sqrt[3]{216x^{9}y^{12}}$$

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

$$\sqrt[3]{216}\sqrt[3]{x^{9}}\sqrt[3]{y^{12}}$$

Raise 216 to the power \frac{1}{3}.

$$6\sqrt[3]{x^{9}}\sqrt[3]{y^{12}}$$

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

$$6x^{9\times \frac{1}{3}}y^{12\times \frac{1}{3}}$$

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

$$6x^{3}y^{12\times \frac{1}{3}}$$

Multiply 12 times \frac{1}{3}.

$$6x^{3}y^{4}$$

Differentiate w.r.t. x

$$18x^{2}y^{4}$$