Solve (frac{2m^{3}n^4}{m^5n^3})^-1

$$( \frac { 2 m ^ { 3 } n ^ { 4 } } { m ^ { 5 } n ^ { 3 } } ) ^ { - 1 }$$

Evaluate

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

Solution Steps

Cancel out m^{3}n^{3} in both numerator and denominator.

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

To raise \frac{2n}{m^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

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

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

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

Calculate 2 to the power of -1 and get \frac{1}{2}.

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

Differentiate w.r.t. n

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