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

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

Evaluate

$$a^{11}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$a^{9}a^{2}$$

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$a^{11}$$

Differentiate w.r.t. a

$$11a^{10}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9}a^{2})$$

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{11})$$

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

$$11a^{11-1}$$

Subtract 1 from 11.

$$11a^{10}$$