Solve m^-3/4n^-3/4/(m^2n)^1/2

$$\frac { m ^ { - 3 / 4 } n ^ { - 3 / 4 } } { ( m ^ { 2 } n ) ^ { 1 / 2 } }$$

Evaluate

$$\frac{1}{n^{\frac{5}{4}}m^{\frac{7}{4}}}$$

Solution Steps

Expand \left(m^{2}n\right)^{\frac{1}{2}}.

$$\frac{m^{-\frac{3}{4}}n^{-\frac{3}{4}}}{\left(m^{2}\right)^{\frac{1}{2}}n^{\frac{1}{2}}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{2} to get 1.

$$\frac{m^{-\frac{3}{4}}n^{-\frac{3}{4}}}{m^{1}n^{\frac{1}{2}}}$$

Calculate m to the power of 1 and get m.

$$\frac{m^{-\frac{3}{4}}n^{-\frac{3}{4}}}{mn^{\frac{1}{2}}}$$

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

$$\frac{1}{n^{\frac{5}{4}}m^{\frac{7}{4}}}$$

Differentiate w.r.t. n

$$-\frac{5}{4m^{\frac{7}{4}}n^{\frac{9}{4}}}$$