Solve (n^2)^4

$$( n ^ { 2 } ) ^ { 4 }$$

Evaluate

$$n^{8}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(n^{2}\right)^{4}$$

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

$$n^{2\times 4}$$

Multiply 2 times 4.

$$n^{8}$$

Differentiate w.r.t. n

$$8n^{7}$$

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).

$$4\left(n^{2}\right)^{4-1}\frac{\mathrm{d}}{\mathrm{d}n}(n^{2})$$

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}.

$$4\left(n^{2}\right)^{3}\times 2n^{2-1}$$

Simplify.

$$8n^{1}\left(n^{2}\right)^{3}$$

For any term t, t^{1}=t.

$$8n\left(n^{2}\right)^{3}$$