Solve (-w^5x^9)^frac{2{3}}

$$( - w ^ { 5 } x ^ { 9 } ) ^ { \frac { 2 } { 3 } }$$

Evaluate

$$w^{\frac{10}{3}}x^{6}$$

Solution Steps

Expand \left(\left(-w^{5}\right)x^{9}\right)^{\frac{2}{3}}.

$$\left(-w^{5}\right)^{\frac{2}{3}}\left(x^{9}\right)^{\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and \frac{2}{3} to get 6.

$$\left(-w^{5}\right)^{\frac{2}{3}}x^{6}$$

Expand \left(-w^{5}\right)^{\frac{2}{3}}.

$$\left(-1\right)^{\frac{2}{3}}\left(w^{5}\right)^{\frac{2}{3}}x^{6}$$

To raise a power to another power, multiply the exponents. Multiply 5 and \frac{2}{3} to get \frac{10}{3}.

$$\left(-1\right)^{\frac{2}{3}}w^{\frac{10}{3}}x^{6}$$

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

$$1w^{\frac{10}{3}}x^{6}$$

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

$$w^{\frac{10}{3}}x^{6}$$

Differentiate w.r.t. x

$$6w^{\frac{10}{3}}x^{5}$$