Solve 30m^{4}n^9div4m^3n^5div(-5mn^2)

$$30 m ^ { 4 } n ^ { 9 } \div 4 m ^ { 3 } n ^ { 5 } \div ( - 5 m n ^ { 2 } )$$

Evaluate

$$-\frac{3m^{6}n^{12}}{2}$$

Solution Steps

Divide 30m^{4}n^{9} by 4 to get \frac{15}{2}m^{4}n^{9}.

$$\frac{\frac{15}{2}m^{4}n^{9}m^{3}n^{5}}{-5mn^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\frac{15}{2}m^{7}n^{9}n^{5}}{-5mn^{2}}$$

To multiply powers of the same base, add their exponents. Add 9 and 5 to get 14.

$$\frac{\frac{15}{2}m^{7}n^{14}}{-5mn^{2}}$$

Cancel out mn^{2} in both numerator and denominator.

$$\frac{\frac{15}{2}m^{6}n^{12}}{-5}$$

Divide \frac{15}{2}m^{6}n^{12} by -5 to get -\frac{3}{2}m^{6}n^{12}.

$$-\frac{3}{2}m^{6}n^{12}$$

Differentiate w.r.t. n

$$-18m^{6}n^{11}$$