Solve (x^3y^9/z^6)^frac{1{3}}

$$( \frac { x ^ { 3 } y ^ { 9 } } { z ^ { 6 } } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{xy^{3}}{z^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

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

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

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

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

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

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

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

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

$$\frac{x^{1}y^{3}}{z^{2}}$$

For any term t, t^{1}=t.

$$\frac{xy^{3}}{z^{2}}$$

Differentiate w.r.t. x

$$\frac{y^{3}}{z^{2}}$$