Solve -4a^3*2a^5=

$$- 4 a ^ { 3 } \cdot 2 a ^ { 5 } =$$

Evaluate

$$-8a^{8}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$-4a^{8}\times 2$$

Multiply -4 and 2 to get -8.

$$-8a^{8}$$

Differentiate w.r.t. a

$$-64a^{7}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-4a^{8}\times 2)$$

Multiply -4 and 2 to get -8.

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

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

$$8\left(-8\right)a^{8-1}$$

Multiply 8 times -8.

$$-64a^{8-1}$$

Subtract 1 from 8.

$$-64a^{7}$$