Solve left(x^-2right)^10

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

Evaluate

$$\frac{1}{x^{20}}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

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

To raise a power to another power, multiply the exponents.

$$x^{-2\times 10}$$

Multiply -2 times 10.

$$\frac{1}{x^{20}}$$

Differentiate w.r.t. x

$$-\frac{20}{x^{21}}$$

Steps Using Chain Rule

If F is the composition of two differentiable functions f\left(u\right) and u=g\left(x\right), that is, if F\left(x\right)=f\left(g\left(x\right)\right), then the derivative of F is the derivative of f with respect to u times the derivative of g with respect to x, that is, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$10\left(x^{-2}\right)^{10-1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{-2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$10\left(x^{-2}\right)^{9}\left(-2\right)x^{-2-1}$$

Simplify.

$$-20x^{-3}\left(x^{-2}\right)^{9}$$