Solve (4a^2)(-8a^3)(a)

$$( 4 a ^ { 2 } ) ( - 8 a ^ { 3 } ) ( a )$$

Evaluate

$$-32a^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$4a^{5}\left(-8\right)a$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$4a^{6}\left(-8\right)$$

Multiply 4 and -8 to get -32.

$$-32a^{6}$$

Differentiate w.r.t. a

$$-192a^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{5}\left(-8\right)a)$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}a}(4a^{6}\left(-8\right))$$

Multiply 4 and -8 to get -32.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-32a^{6})$$

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

$$6\left(-32\right)a^{6-1}$$

Multiply 6 times -32.

$$-192a^{6-1}$$

Subtract 1 from 6.

$$-192a^{5}$$