Solve (a^{2})^3+(a^2)^2*a^2

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

Evaluate

$$2a^{6}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$a^{6}+\left(a^{2}\right)^{2}a^{2}$$

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

$$a^{6}+a^{4}a^{2}$$

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

$$a^{6}+a^{6}$$

Combine a^{6} and a^{6} to get 2a^{6}.

$$2a^{6}$$

Differentiate w.r.t. a

$$12a^{5}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+\left(a^{2}\right)^{2}a^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+a^{4}a^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}+a^{6})$$

Combine a^{6} and a^{6} to get 2a^{6}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a^{6})$$

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

$$6\times 2a^{6-1}$$

Multiply 6 times 2.

$$12a^{6-1}$$

Subtract 1 from 6.

$$12a^{5}$$