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

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

Evaluate

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

Solution Steps

Expand \left(m^{4}n^{3}\right)^{-1}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and -1 to get -4.

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

To raise a power to another power, multiply the exponents. Multiply 3 and -1 to get -3.

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

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

$$\frac{n^{-5}m^{2}}{n^{-3}}$$

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

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

Differentiate w.r.t. n

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