Solve (-3a^3)(5a^5)

$$( - 3 a ^ { 3 } ) ( 5 a ^ { 5 } )$$

Evaluate

$$-15a^{8}$$

Solution Steps

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

$$-3a^{8}\times 5$$

Multiply -3 and 5 to get -15.

$$-15a^{8}$$

Differentiate w.r.t. a

$$-120a^{7}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(-3a^{8}\times 5)$$

Multiply -3 and 5 to get -15.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-15a^{8})$$

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

$$8\left(-15\right)a^{8-1}$$

Multiply 8 times -15.

$$-120a^{8-1}$$

Subtract 1 from 8.

$$-120a^{7}$$