Solve 18m^3n^3/12mn^3

$$\frac { 18 m ^ { 3 } n ^ { 3 } } { 12 m n ^ { 3 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{18^{1}m^{3}n^{3}}{12^{1}m^{1}n^{3}}$$

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

$$\frac{18^{1}}{12^{1}}m^{3-1}n^{3-3}$$

Subtract 1 from 3.

$$\frac{18^{1}}{12^{1}}m^{2}n^{3-3}$$

Subtract 3 from 3.

$$\frac{18^{1}}{12^{1}}m^{2}n^{0}$$

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

$$\frac{18^{1}}{12^{1}}m^{2}$$

Reduce the fraction \frac{18}{12} to lowest terms by extracting and canceling out 6.

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

Differentiate w.r.t. m

$$3m$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{18n^{3}}{12n^{3}}m^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{3}{2}m^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2\times \frac{3}{2}m^{2-1}$$

Do the arithmetic.

$$3m^{1}$$

For any term t, t^{1}=t.

$$3m$$