Solve (s^-5)^3

$$( s ^ { - 5 } ) ^ { 3 }$$

Evaluate

$$\frac{1}{s^{15}}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

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

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

$$s^{-5\times 3}$$

Multiply -5 times 3.

$$\frac{1}{s^{15}}$$

Differentiate w.r.t. s

$$-\frac{15}{s^{16}}$$

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).

$$3\left(s^{-5}\right)^{3-1}\frac{\mathrm{d}}{\mathrm{d}s}(s^{-5})$$

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}.

$$3\left(s^{-5}\right)^{2}\left(-5\right)s^{-5-1}$$

Simplify.

$$-15s^{-6}\left(s^{-5}\right)^{2}$$