Solve frac{2^{-6}m^{14}n^6}{5^-3m^6n^14}

$$\frac { 2 ^ { - 6 } m ^ { 14 } n ^ { 6 } } { 5 ^ { - 3 } m ^ { 6 } n ^ { 14 } }$$

Evaluate

$$\frac{125\times \left(\frac{m}{n}\right)^{8}}{64}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{-6}m^{14}n^{6}}{5^{-3}m^{6}n^{14}}$$

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

$$\frac{2^{-6}}{5^{-3}}m^{14-6}n^{6-14}$$

Subtract 6 from 14.

$$\frac{2^{-6}}{5^{-3}}m^{8}n^{6-14}$$

Subtract 14 from 6.

$$\frac{2^{-6}}{5^{-3}}m^{8}n^{-8}$$

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

$$\frac{125}{64}m^{8}\times \frac{1}{n^{8}}$$

Differentiate w.r.t. n

$$-\frac{125m^{8}}{8n^{9}}$$