Solve (a^2)^2*(a^2)^2

$$( a ^ { 2 } ) ^ { 2 } \cdot ( a ^ { 2 } ) ^ { 2 }$$

Evaluate

$$a^{8}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(a^{2}\right)^{2}\left(a^{2}\right)^{2}$$

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

$$a^{2\times 2}a^{2\times 2}$$

Multiply 2 times 2.

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

Multiply 2 times 2.

$$a^{4}a^{4}$$

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

$$a^{4+4}$$

Add the exponents 4 and 4.

$$a^{8}$$

Differentiate w.r.t. a

$$8a^{7}$$

Steps Using Definition of a Derivative

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{4}a^{4})$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

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

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

$$8a^{8-1}$$

Subtract 1 from 8.

$$8a^{7}$$