Solve (-x^9y^10)^frac{1{3}}

$$( - x ^ { 9 } y ^ { 10 } ) ^ { \frac { 1 } { 3 } }$$

Evaluate

$$-x^{3}y^{\frac{10}{3}}$$

Solution Steps

Expand \left(\left(-x^{9}\right)y^{10}\right)^{\frac{1}{3}}.

$$\left(-x^{9}\right)^{\frac{1}{3}}\left(y^{10}\right)^{\frac{1}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and \frac{1}{3} to get \frac{10}{3}.

$$\left(-x^{9}\right)^{\frac{1}{3}}y^{\frac{10}{3}}$$

Expand \left(-x^{9}\right)^{\frac{1}{3}}.

$$\left(-1\right)^{\frac{1}{3}}\left(x^{9}\right)^{\frac{1}{3}}y^{\frac{10}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and \frac{1}{3} to get 3.

$$\left(-1\right)^{\frac{1}{3}}x^{3}y^{\frac{10}{3}}$$

Calculate -1 to the power of \frac{1}{3} and get -1.

$$-x^{3}y^{\frac{10}{3}}$$

Differentiate w.r.t. x

$$-3x^{2}y^{\frac{10}{3}}$$