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

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

Evaluate

$$3m^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

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

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

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

Subtract 2 from 4.

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

Subtract 2 from 2.

$$\frac{6^{1}}{2^{1}}m^{2}n^{0}$$

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

$$\frac{6^{1}}{2^{1}}m^{2}$$

Divide 6 by 2.

$$3m^{2}$$

Differentiate w.r.t. m

$$6m$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$6m^{1}$$

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

$$6m$$