Solve frac{m^{0}n^4}{3mn^2*m^2n^4}

$$\frac { m ^ { 0 } n ^ { 4 } } { 3 m n ^ { 2 } \cdot m ^ { 2 } n ^ { 4 } }$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{m^{0}n^{4}}{3m^{3}n^{2}n^{4}}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{m^{0}n^{4}}{3m^{3}n^{6}}$$

Cancel out n^{4} in both numerator and denominator.

$$\frac{m^{0}}{3n^{2}m^{3}}$$

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

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

Differentiate w.r.t. m

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