Solve (a^4)(a^7)(a^6)

$$( a ^ { 4 } ) ( a ^ { 7 } ) ( a ^ { 6 } )$$

Evaluate

$$a^{17}$$

Steps Using Product of Powers Property

Use the rules of exponents to simplify the expression.

$$a^{4}a^{7}a^{6}$$

Use the Multiplication Rule for Exponents.

$$a^{4+7+6}$$

Add the exponents 4 and 7.

$$a^{11+6}$$

Add the exponents 11 and 6.

$$a^{17}$$

Differentiate w.r.t. a

$$17a^{16}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{11}a^{6})$$

To multiply powers of the same base, add their exponents. Add 11 and 6 to get 17.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a^{17})$$

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

$$17a^{17-1}$$

Subtract 1 from 17.

$$17a^{16}$$