Solve (9p^4)(-8p^2)

$$( 9 p ^ { 4 } ) ( - 8 p ^ { 2 } )$$

Evaluate

$$-72p^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$9p^{6}\left(-8\right)$$

Multiply 9 and -8 to get -72.

$$-72p^{6}$$

Differentiate w.r.t. p

$$-432p^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}p}(9p^{6}\left(-8\right))$$

Multiply 9 and -8 to get -72.

$$\frac{\mathrm{d}}{\mathrm{d}p}(-72p^{6})$$

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

$$6\left(-72\right)p^{6-1}$$

Multiply 6 times -72.

$$-432p^{6-1}$$

Subtract 1 from 6.

$$-432p^{5}$$