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

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

Evaluate

$$x^{6}$$

Solution Steps

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

$$x^{2}x^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$x^{6}$$

Differentiate w.r.t. x

$$6x^{5}$$

Steps Using Definition of a Derivative

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

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

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

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

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

$$6x^{6-1}$$

Subtract 1 from 6.

$$6x^{5}$$