Solve (1)(m^4)^3*m^2

$$( 1 ) ( m ^ { 4 } ) ^ { 3 } \cdot m ^ { 2 }$$

Evaluate

$$m^{14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$1m^{12}m^{2}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$1m^{14}$$

For any term t, t\times 1=t and 1t=t.

$$m^{14}$$

Differentiate w.r.t. m

$$14m^{13}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}m}(1m^{12}m^{2})$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}m}(1m^{14})$$

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

$$14m^{14-1}$$

Subtract 1 from 14.

$$14m^{13}$$