Evaluate
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Differentiate w.r.t. m
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\frac{2^{-6}m^{13}n^{7}}{5^{-2}m^{7}n^{13}}
Use the rules of exponents to simplify the expression.
\frac{2^{-6}}{5^{-2}}m^{13-7}n^{7-13}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{2^{-6}}{5^{-2}}m^{6}n^{7-13}
Subtract 7 from 13.
\frac{2^{-6}}{5^{-2}}m^{6}n^{-6}
Subtract 13 from 7.
\frac{25}{64}m^{6}\times \left(\frac{1}{n^{6}}\right)
Divide \frac{1}{64} by \frac{1}{25} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{25}.
\frac{\mathrm{d}}{\mathrm{d}m}(\frac{n^{7}}{64\times \left(\frac{n^{13}}{25}\right)}m^{13-7})
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\frac{\mathrm{d}}{\mathrm{d}m}(\frac{25}{64n^{6}}m^{6})
Do the arithmetic.
6\times \left(\frac{25}{64n^{6}}\right)m^{6-1}
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.
\frac{75}{32n^{6}}m^{5}
Do the arithmetic.