Solve (-x^{4})^{2}-(x^{5})^2divx^2-(-x)^3*(-x^5)

$$( - x ^ { 4 } ) ^ { 2 } - ( x ^ { 5 } ) ^ { 2 } \div x ^ { 2 } - ( - x ) ^ { 3 } \cdot ( - x ^ { 5 } )$$

Evaluate

$$-x^{8}$$

Solution Steps

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

$$\left(-x^{4}\right)^{2}-\frac{x^{10}}{x^{2}}-\left(-x\right)^{3}\left(-x^{5}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$\left(-x^{4}\right)^{2}-x^{8}-\left(-x\right)^{3}\left(-x^{5}\right)$$

Calculate -x^{4} to the power of 2 and get \left(x^{4}\right)^{2}.

$$\left(x^{4}\right)^{2}-x^{8}-\left(-x\right)^{3}\left(-x^{5}\right)$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}-x^{8}-\left(-x\right)^{3}\left(-x^{5}\right)$$

Subtract x^{8} from x^{8} to get 0.

$$0-\left(-x\right)^{3}\left(-x^{5}\right)$$

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

$$0-\left(-1\right)^{3}x^{3}\left(-1\right)x^{5}$$

Calculate -1 to the power of 3 and get -1.

$$0-\left(-x^{3}\left(-1\right)x^{5}\right)$$

Multiply -1 and -1 to get 1.

$$0+x^{3}\left(-1\right)x^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$0+x^{8}\left(-1\right)$$

Anything plus zero gives itself.

$$x^{8}\left(-1\right)$$

Expand

$$-x^{8}$$

Solution Steps

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

$$\left(-x^{4}\right)^{2}-\frac{x^{10}}{x^{2}}-\left(-x\right)^{3}\left(-x^{5}\right)$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$\left(-x^{4}\right)^{2}-x^{8}-\left(-x\right)^{3}\left(-x^{5}\right)$$

Calculate -x^{4} to the power of 2 and get \left(x^{4}\right)^{2}.

$$\left(x^{4}\right)^{2}-x^{8}-\left(-x\right)^{3}\left(-x^{5}\right)$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}-x^{8}-\left(-x\right)^{3}\left(-x^{5}\right)$$

Subtract x^{8} from x^{8} to get 0.

$$0-\left(-x\right)^{3}\left(-x^{5}\right)$$

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

$$0-\left(-1\right)^{3}x^{3}\left(-1\right)x^{5}$$

Calculate -1 to the power of 3 and get -1.

$$0-\left(-x^{3}\left(-1\right)x^{5}\right)$$

Multiply -1 and -1 to get 1.

$$0+x^{3}\left(-1\right)x^{5}$$

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$0+x^{8}\left(-1\right)$$

Anything plus zero gives itself.

$$x^{8}\left(-1\right)$$