Solve 36m^4n^4/6m^2n

$$\frac { 36 m ^ { 4 } n ^ { 4 } } { 6 m ^ { 2 } n }$$

Evaluate

$$6m^{2}n^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{36^{1}m^{4}n^{4}}{6^{1}m^{2}n^{1}}$$

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

$$\frac{36^{1}}{6^{1}}m^{4-2}n^{4-1}$$

Subtract 2 from 4.

$$\frac{36^{1}}{6^{1}}m^{2}n^{4-1}$$

Subtract 1 from 4.

$$\frac{36^{1}}{6^{1}}m^{2}n^{3}$$

Divide 36 by 6.

$$6m^{2}n^{3}$$

Differentiate w.r.t. m

$$12mn^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}m}(\frac{36n^{4}}{6n}m^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}m}(6n^{3}m^{2})$$

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}.

$$2\times 6n^{3}m^{2-1}$$

Do the arithmetic.

$$12n^{3}m^{1}$$

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

$$12n^{3}m$$