Solve (m^5)^2*m^4

$$( m ^ { 5 } ) ^ { 2 } \cdot m ^ { 4 }$$

Evaluate

$$m^{14}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$m^{10}m^{4}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$m^{14}$$

Differentiate w.r.t. m

$$14m^{13}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m^{10}m^{4})$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

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

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

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

Subtract 1 from 14.

$$14m^{13}$$