Solve (8x^3)(-2x^6)

$$(8 { x }^{ 3 } )(-2 { x }^{ 6 } )$$

Evaluate

$$-16x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$8x^{9}\left(-2\right)$$

Multiply 8 and -2 to get -16.

$$-16x^{9}$$

Differentiate w.r.t. x

$$-144x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{9}\left(-2\right))$$

Multiply 8 and -2 to get -16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-16x^{9})$$

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

$$9\left(-16\right)x^{9-1}$$

Multiply 9 times -16.

$$-144x^{9-1}$$

Subtract 1 from 9.

$$-144x^{8}$$