Solve (u^4)^2(u^8)^2

$$( u ^ { 4 } ) ^ { 2 } ( u ^ { 8 } ) ^ { 2 }$$

Evaluate

$$u^{24}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(u^{4}\right)^{2}\left(u^{8}\right)^{2}$$

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

$$u^{4\times 2}u^{8\times 2}$$

Multiply 4 times 2.

$$u^{8}u^{8\times 2}$$

Multiply 8 times 2.

$$u^{8}u^{16}$$

To multiply powers of the same base, add their exponents.

$$u^{8+16}$$

Add the exponents 8 and 16.

$$u^{24}$$

Differentiate w.r.t. u

$$24u^{23}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{8}\left(u^{8}\right)^{2})$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{8}u^{16})$$

To multiply powers of the same base, add their exponents. Add 8 and 16 to get 24.

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

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

$$24u^{24-1}$$

Subtract 1 from 24.

$$24u^{23}$$