Solve frac{m^{-29}n^0*mn^-1}{m^53n^-66}

$$\frac { m ^ { - 29 } n ^ { 0 } \cdot m n ^ { - 1 } } { m ^ { 53 } n ^ { - 66 } }$$

Evaluate

$$\frac{n^{65}}{m^{81}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -29 and 1 to get -28.

$$\frac{m^{-28}n^{0}n^{-1}}{m^{53}n^{-66}}$$

To multiply powers of the same base, add their exponents. Add 0 and -1 to get -1.

$$\frac{m^{-28}n^{-1}}{m^{53}n^{-66}}$$

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

$$\frac{m^{-28}n^{65}}{m^{53}}$$

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

$$\frac{n^{65}}{m^{81}}$$

Differentiate w.r.t. n

$$\frac{65n^{64}}{m^{81}}$$