Solve 14m^{2}n^2div(-21m^5n)*6m^5n^2

$$14 m ^ { 2 } n ^ { 2 } \div ( - 21 m ^ { 5 } n ) \times 6 m ^ { 5 } n ^ { 2 }$$

Evaluate

$$-4m^{2}n^{3}$$

Solution Steps

Cancel out 7nm^{2} in both numerator and denominator.

$$\frac{2n}{-3m^{3}}\times 6m^{5}n^{2}$$

Express \frac{2n}{-3m^{3}}\times 6 as a single fraction.

$$\frac{2n\times 6}{-3m^{3}}m^{5}n^{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2\times 2n}{-m^{3}}m^{5}n^{2}$$

Express \frac{2\times 2n}{-m^{3}}m^{5} as a single fraction.

$$\frac{2\times 2nm^{5}}{-m^{3}}n^{2}$$

Cancel out m^{3} in both numerator and denominator.

$$\frac{2\times 2nm^{2}}{-1}n^{2}$$

Express \frac{2\times 2nm^{2}}{-1}n^{2} as a single fraction.

$$\frac{2\times 2nm^{2}n^{2}}{-1}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{2\times 2n^{3}m^{2}}{-1}$$

Multiply 2 and 2 to get 4.

$$\frac{4n^{3}m^{2}}{-1}$$

Anything divided by -1 gives its opposite.

$$-4n^{3}m^{2}$$

Differentiate w.r.t. n

$$-12\left(mn\right)^{2}$$