Solve (-4p^7)(9p^8)

$$( - 4 p ^ { 7 } ) ( 9 p ^ { 8 } )$$

Evaluate

$$-36p^{15}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 8 to get 15.

$$-4p^{15}\times 9$$

Multiply -4 and 9 to get -36.

$$-36p^{15}$$

Differentiate w.r.t. p

$$-540p^{14}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 8 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-4p^{15}\times 9)$$

Multiply -4 and 9 to get -36.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-36p^{15})$$

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

$$15\left(-36\right)p^{15-1}$$

Multiply 15 times -36.

$$-540p^{15-1}$$

Subtract 1 from 15.

$$-540p^{14}$$