Solve (1/6a^5)(-3a^2)4a^7

$$( \frac { 1 } { 6 } a ^ { 5 } ) ( - 3 a ^ { 2 } ) 4 a ^ { 7 }$$

Evaluate

$$-2a^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{1}{6}a^{7}\left(-3\right)\times 4a^{7}$$

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$\frac{1}{6}a^{14}\left(-3\right)\times 4$$

Multiply \frac{1}{6} and -3 to get -\frac{1}{2}.

$$-\frac{1}{2}a^{14}\times 4$$

Multiply -\frac{1}{2} and 4 to get -2.

$$-2a^{14}$$

Differentiate w.r.t. a

$$-28a^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{6}a^{7}\left(-3\right)\times 4a^{7})$$

To multiply powers of the same base, add their exponents. Add 7 and 7 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{6}a^{14}\left(-3\right)\times 4)$$

Multiply \frac{1}{6} and -3 to get -\frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-\frac{1}{2}a^{14}\times 4)$$

Multiply -\frac{1}{2} and 4 to get -2.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-2a^{14})$$

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

$$14\left(-2\right)a^{14-1}$$

Multiply 14 times -2.

$$-28a^{14-1}$$

Subtract 1 from 14.

$$-28a^{13}$$