Solve ((x^2)^3)^4=

$$( ( x ^ { 2 } ) ^ { 3 } ) ^ { 4 } =$$

Evaluate

$$x^{24}$$

Steps for Raising Power to Another Power

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(x^{6}\right)^{4}$$

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

$$x^{6\times 4}$$

Multiply 6 times 4.

$$x^{24}$$

Differentiate w.r.t. x

$$24x^{23}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(x^{6}\right)^{4})$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{24})$$

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

$$24x^{24-1}$$

Subtract 1 from 24.

$$24x^{23}$$