Solve m^7n^2/m^3n^2

$$\frac { m ^ { 7 } n ^ { 2 } } { m ^ { 3 } n ^ { 2 } }$$

Evaluate

$$m^{4}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{m^{7}n^{2}}{m^{3}n^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$m^{7-3}n^{2-2}$$

Subtract 3 from 7.

$$m^{4}n^{2-2}$$

Subtract 2 from 2.

$$m^{4}n^{0}$$

For any number a except 0, a^{0}=1.

$$m^{4}$$

Differentiate w.r.t. m

$$4m^{3}$$

Steps Using Definition of a Derivative

Cancel out n^{2}m^{3} in both numerator and denominator.

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

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

$$4m^{4-1}$$

Subtract 1 from 4.

$$4m^{3}$$