Solve frac{2^{-6}m^{11}n^6}{5^-3m^6n^11}

$$\frac { 2 ^ { - 6 } m ^ { 11 } n ^ { 6 } } { 5 ^ { - 3 } m ^ { 6 } n ^ { 11 } }$$

Evaluate

$$\frac{125\times \left(\frac{m}{n}\right)^{5}}{64}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{-6}m^{11}n^{6}}{5^{-3}m^{6}n^{11}}$$

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

$$\frac{2^{-6}}{5^{-3}}m^{11-6}n^{6-11}$$

Subtract 6 from 11.

$$\frac{2^{-6}}{5^{-3}}m^{5}n^{6-11}$$

Subtract 11 from 6.

$$\frac{2^{-6}}{5^{-3}}m^{5}n^{-5}$$

Divide \frac{1}{64} by \frac{1}{125} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{125}.

$$\frac{125}{64}m^{5}\times \frac{1}{n^{5}}$$

Differentiate w.r.t. n

$$-\frac{625m^{5}}{64n^{6}}$$