Solve (n^10)^20

$$( n ^ { 10 } ) ^ { 20 }$$

Evaluate

$$n^{200}$$

Steps for Raising Power to Another Power

Use the rules of exponents to simplify the expression.

$$\left(n^{10}\right)^{20}$$

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

$$n^{10\times 20}$$

Multiply 10 times 20.

$$n^{200}$$

Differentiate w.r.t. n

$$200n^{199}$$

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).

$$20\left(n^{10}\right)^{20-1}\frac{\mathrm{d}}{\mathrm{d}n}(n^{10})$$

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}.

$$20\left(n^{10}\right)^{19}\times 10n^{10-1}$$

Simplify.

$$200n^{9}\left(n^{10}\right)^{19}$$