Solve a^2*(a^4)^2

$$a ^ { 2 } \cdot ( a ^ { 4 } ) ^ { 2 }$$

Evaluate

$$a^{10}$$

Solution Steps

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

$$a^{2}a^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$a^{10}$$

Differentiate w.r.t. a

$$10a^{9}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{2}a^{8})$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{10})$$

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

$$10a^{10-1}$$

Subtract 1 from 10.

$$10a^{9}$$