Solve (-x^5)^2+(-x^2)^5

$$( - x ^ { 5 } ) ^ { 2 } + ( - x ^ { 2 } ) ^ { 5 }$$

Evaluate

$$0$$

Solution Steps

Calculate -x^{5} to the power of 2 and get \left(x^{5}\right)^{2}.

$$\left(x^{5}\right)^{2}+\left(-x^{2}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$x^{10}+\left(-x^{2}\right)^{5}$$

Expand \left(-x^{2}\right)^{5}.

$$x^{10}+\left(-1\right)^{5}\left(x^{2}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$x^{10}+\left(-1\right)^{5}x^{10}$$

Calculate -1 to the power of 5 and get -1.

$$x^{10}-x^{10}$$

Combine x^{10} and -x^{10} to get 0.

$$0$$

Factor

$$0$$