Solve (7m^3)(4m^4)

$$( 7 m ^ { 3 } ) ( 4 m ^ { 4 } )$$

Evaluate

$$28m^{7}$$

Solution Steps

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

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

Multiply 7 and 4 to get 28.

$$28m^{7}$$

Differentiate w.r.t. m

$$196m^{6}$$

Steps Using Definition of a Derivative

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

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

Multiply 7 and 4 to get 28.

$$\frac{\mathrm{d}}{\mathrm{d}m}(28m^{7})$$

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

$$7\times 28m^{7-1}$$

Multiply 7 times 28.

$$196m^{7-1}$$

Subtract 1 from 7.

$$196m^{6}$$