Solve -10(x^2)^-2/-5(x^3)^0

$$\frac { - 10 ( x ^ { 2 } ) ^ { - 2 } } { - 5 ( x ^ { 3 } ) ^ { 0 } }$$

Evaluate

$$\frac{2}{x^{4}}$$

Solution Steps

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

$$\frac{-10x^{-4}}{-5\left(x^{3}\right)^{0}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 0 to get 0.

$$\frac{-10x^{-4}}{-5x^{0}}$$

Cancel out 5 in both numerator and denominator.

$$\frac{-2x^{-4}}{-x^{0}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{-2}{-x^{4}}$$

Differentiate w.r.t. x

$$-\frac{8}{x^{5}}$$