Solve (n^-3)^4

$$( n ^ { - 3 } ) ^ { 4 }$$

Evaluate

$$\frac{1}{n^{12}}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(n^{-3}\right)^{4}$$

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

$$n^{-3\times 4}$$

Multiply -3 times 4.

$$\frac{1}{n^{12}}$$

Differentiate w.r.t. n

$$-\frac{12}{n^{13}}$$

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).

$$4\left(n^{-3}\right)^{4-1}\frac{\mathrm{d}}{\mathrm{d}n}(n^{-3})$$

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}.

$$4\left(n^{-3}\right)^{3}\left(-3\right)n^{-3-1}$$

Simplify.

$$-12n^{-4}\left(n^{-3}\right)^{3}$$