Solve (6m^4)(8m^2)

$$( 6 m ^ { 4 } ) ( 8 m ^ { 2 } )$$

Evaluate

$$48m^{6}$$

Solution Steps

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

$$6m^{6}\times 8$$

Multiply 6 and 8 to get 48.

$$48m^{6}$$

Differentiate w.r.t. m

$$288m^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(6m^{6}\times 8)$$

Multiply 6 and 8 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}m}(48m^{6})$$

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

$$6\times 48m^{6-1}$$

Multiply 6 times 48.

$$288m^{6-1}$$

Subtract 1 from 6.

$$288m^{5}$$