Solve (-1x^6y^18)^frac{2{3}}

$$( - 1 x ^ { 6 } y ^ { 18 } ) ^ { \frac { 2 } { 3 } }$$

Evaluate

$$x^{4}y^{12}$$

Solution Steps

Expand \left(-x^{6}y^{18}\right)^{\frac{2}{3}}.

$$\left(-1\right)^{\frac{2}{3}}\left(x^{6}\right)^{\frac{2}{3}}\left(y^{18}\right)^{\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and \frac{2}{3} to get 4.

$$\left(-1\right)^{\frac{2}{3}}x^{4}\left(y^{18}\right)^{\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 18 and \frac{2}{3} to get 12.

$$\left(-1\right)^{\frac{2}{3}}x^{4}y^{12}$$

Calculate -1 to the power of \frac{2}{3} and get 1.

$$1x^{4}y^{12}$$

For any term t, t\times 1=t and 1t=t.

$$x^{4}y^{12}$$

Differentiate w.r.t. x

$$4x^{3}y^{12}$$