Solve a^7a^2aa^3=

$$a ^ { 7 } a ^ { 2 } a a ^ { 3 } =$$

Evaluate

$$a^{13}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$a^{9}aa^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$a^{10}a^{3}$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$a^{13}$$

Differentiate w.r.t. a

$$13a^{12}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{9}aa^{3})$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{10}a^{3})$$

To multiply powers of the same base, add their exponents. Add 10 and 3 to get 13.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{13})$$

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

$$13a^{13-1}$$

Subtract 1 from 13.

$$13a^{12}$$