Solve (a^2)^4+a^4*a^3*a

$$( a ^ { 2 } ) ^ { 4 } + a ^ { 4 } \cdot a ^ { 3 } \cdot a$$

Evaluate

$$2a^{8}$$

Solution Steps

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

$$a^{8}+a^{4}a^{3}a$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$a^{8}+a^{7}a$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

$$a^{8}+a^{8}$$

Combine a^{8} and a^{8} to get 2a^{8}.

$$2a^{8}$$

Differentiate w.r.t. a

$$16a^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{8}+a^{4}a^{3}a)$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{8}+a^{7}a)$$

To multiply powers of the same base, add their exponents. Add 7 and 1 to get 8.

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

Combine a^{8} and a^{8} to get 2a^{8}.

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

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

$$8\times 2a^{8-1}$$

Multiply 8 times 2.

$$16a^{8-1}$$

Subtract 1 from 8.

$$16a^{7}$$