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

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

Evaluate

$$a^{12}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(a^{2}\right)^{3}\left(a^{3}\right)^{2}$$

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

$$a^{2\times 3}a^{3\times 2}$$

Multiply 2 times 3.

$$a^{6}a^{3\times 2}$$

Multiply 3 times 2.

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

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

$$a^{6+6}$$

Add the exponents 6 and 6.

$$a^{12}$$

Differentiate w.r.t. a

$$12a^{11}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{6}\left(a^{3}\right)^{2})$$

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

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

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{12})$$

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

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

Subtract 1 from 12.

$$12a^{11}$$