Solve ((x^2)^2)^2

$$( ( x ^ { 2 } ) ^ { 2 } ) ^ { 2 }$$

Evaluate

$$x^{8}$$

Steps for Raising Power to Another Power

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

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

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

Multiply 4 times 2.

$$x^{8}$$

Differentiate w.r.t. x

$$8x^{7}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{4}\right)^{2})$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8})$$

The derivative of ax^{n} is nax^{n-1}.

$$8x^{8-1}$$

Subtract 1 from 8.

$$8x^{7}$$