Solve frac{10m^{6}n^-5p^-1}{5m^-7p^8}

$$\frac { 10 m ^ { 6 } n ^ { - 5 } p ^ { - 1 } } { 5 m ^ { - 7 } p ^ { 8 } }$$

Evaluate

$$\frac{2m^{13}}{n^{5}p^{9}}$$

Solution Steps

Cancel out 5 in both numerator and denominator.

$$\frac{2n^{-5}\times \frac{1}{p}m^{6}}{m^{-7}p^{8}}$$

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

$$\frac{2n^{-5}\times \frac{1}{p}m^{13}}{p^{8}}$$

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

$$\frac{2n^{-5}m^{13}}{p^{9}}$$

Differentiate w.r.t. n

$$-\frac{10m^{13}}{n^{6}p^{9}}$$