Solve 7m/6n^25x/12n^31/9xm

$$\frac { 7 m } { 6 n ^ { 2 } } \frac { 5 x } { 12 n ^ { 3 } } \frac { 1 } { 9 x m }$$

Evaluate

$$\frac{35}{648n^{5}}$$

Solution Steps

Multiply \frac{7m}{6n^{2}} times \frac{5x}{12n^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7m\times 5x}{6n^{2}\times 12n^{3}}\times \frac{1}{9xm}$$

Multiply \frac{7m\times 5x}{6n^{2}\times 12n^{3}} times \frac{1}{9xm} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7m\times 5x}{6n^{2}\times 12n^{3}\times 9xm}$$

Cancel out mx in both numerator and denominator.

$$\frac{5\times 7}{6\times 9\times 12n^{2}n^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{5\times 7}{6\times 9\times 12n^{5}}$$

Multiply 5 and 7 to get 35.

$$\frac{35}{6\times 9\times 12n^{5}}$$

Multiply 6 and 9 to get 54.

$$\frac{35}{54\times 12n^{5}}$$

Multiply 54 and 12 to get 648.

$$\frac{35}{648n^{5}}$$

Differentiate w.r.t. n

$$-\frac{175}{648n^{6}}$$