Solve a^9*a^7*a^3=

$$a ^ { 9 } \times a ^ { 7 } \times a ^ { 3 } =$$

Evaluate

$$a^{19}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{9}a^{7}a^{3}$$

Use the Multiplication Rule for Exponents.

$$a^{9+7+3}$$

Add the exponents 9 and 7.

$$a^{16+3}$$

Add the exponents 16 and 3.

$$a^{19}$$

Differentiate w.r.t. a

$$19a^{18}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 9 and 7 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{16}a^{3})$$

To multiply powers of the same base, add their exponents. Add 16 and 3 to get 19.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{19})$$

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

$$19a^{19-1}$$

Subtract 1 from 19.

$$19a^{18}$$