Solve (4m^3)(2m^4)=

$$( 4 m ^ { 3 } ) ( 2 m ^ { 4 } ) =$$

Evaluate

$$8m^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$4m^{7}\times 2$$

Multiply 4 and 2 to get 8.

$$8m^{7}$$

Differentiate w.r.t. m

$$56m^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}m}(4m^{7}\times 2)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}m}(8m^{7})$$

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

$$7\times 8m^{7-1}$$

Multiply 7 times 8.

$$56m^{7-1}$$

Subtract 1 from 7.

$$56m^{6}$$