Solve frac{2^{-6}m^{13}n^7}{5^-2m^7n^13}

$$\frac { 2 ^ { - 6 } m ^ { 13 } n ^ { 7 } } { 5 ^ { - 2 } m ^ { 7 } n ^ { 13 } }$$

Evaluate

$$\frac{25\times \left(\frac{m}{n}\right)^{6}}{64}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{2^{-6}m^{13}n^{7}}{5^{-2}m^{7}n^{13}}$$

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

$$\frac{2^{-6}}{5^{-2}}m^{13-7}n^{7-13}$$

Subtract 7 from 13.

$$\frac{2^{-6}}{5^{-2}}m^{6}n^{7-13}$$

Subtract 13 from 7.

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

Divide \frac{1}{64} by \frac{1}{25} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{25}.

$$\frac{25}{64}m^{6}\times \frac{1}{n^{6}}$$

Differentiate w.r.t. n

$$-\frac{75m^{6}}{32n^{7}}$$