Solve 4a*(-8a^3)

$$4 a \cdot ( - 8 a ^ { 3 } )$$

Evaluate

$$-32a^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

Multiply 4 and -8 to get -32.

$$-32a^{4}$$

Differentiate w.r.t. a

$$-128a^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

Multiply 4 and -8 to get -32.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-32a^{4})$$

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

$$4\left(-32\right)a^{4-1}$$

Multiply 4 times -32.

$$-128a^{4-1}$$

Subtract 1 from 4.

$$-128a^{3}$$