Solve (u^-2)^7

$$( u ^ { - 2 } ) ^ { 7 }$$

Evaluate

$$\frac{1}{u^{14}}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(u^{-2}\right)^{7}$$

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

$$u^{-2\times 7}$$

Multiply -2 times 7.

$$\frac{1}{u^{14}}$$

Differentiate w.r.t. u

$$-\frac{14}{u^{15}}$$

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).

$$7\left(u^{-2}\right)^{7-1}\frac{\mathrm{d}}{\mathrm{d}u}(u^{-2})$$

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}.

$$7\left(u^{-2}\right)^{6}\left(-2\right)u^{-2-1}$$

Simplify.

$$-14u^{-3}\left(u^{-2}\right)^{6}$$