Solve (-x^5)^4+(-x^4)^5

$$( - x ^ { 5 } ) ^ { 4 } + ( - x ^ { 4 } ) ^ { 5 }$$

Evaluate

$$0$$

Solution Steps

Expand \left(-x^{5}\right)^{4}.

$$\left(-1\right)^{4}\left(x^{5}\right)^{4}+\left(-x^{4}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\left(-1\right)^{4}x^{20}+\left(-x^{4}\right)^{5}$$

Calculate -1 to the power of 4 and get 1.

$$1x^{20}+\left(-x^{4}\right)^{5}$$

Expand \left(-x^{4}\right)^{5}.

$$1x^{20}+\left(-1\right)^{5}\left(x^{4}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$1x^{20}+\left(-1\right)^{5}x^{20}$$

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

$$1x^{20}-x^{20}$$

Combine 1x^{20} and -x^{20} to get 0.

$$0$$

Factor

$$0$$