Solve 15mn^2/12mn*(2mn)^2/10mn^3

$$\frac { 15 m n ^ { 2 } } { 12 m n } \times \frac { ( 2 m n ) ^ { 2 } } { 10 m n ^ { 3 } }$$

Evaluate

$$\frac{m}{2}$$

Solution Steps

Cancel out 3mn in both numerator and denominator.

$$\frac{5n}{4}\times \frac{\left(2mn\right)^{2}}{10mn^{3}}$$

Expand \left(2mn\right)^{2}.

$$\frac{5n}{4}\times \frac{2^{2}m^{2}n^{2}}{10mn^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{5n}{4}\times \frac{4m^{2}n^{2}}{10mn^{3}}$$

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

$$\frac{5n}{4}\times \frac{2m}{5n}$$

Multiply \frac{5n}{4} times \frac{2m}{5n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5n\times 2m}{4\times 5n}$$

Cancel out 2\times 5n in both numerator and denominator.

$$\frac{m}{2}$$

Expand

$$\frac{m}{2}$$

Solution Steps

Cancel out 3mn in both numerator and denominator.

$$\frac{5n}{4}\times \frac{\left(2mn\right)^{2}}{10mn^{3}}$$

Expand \left(2mn\right)^{2}.

$$\frac{5n}{4}\times \frac{2^{2}m^{2}n^{2}}{10mn^{3}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{5n}{4}\times \frac{4m^{2}n^{2}}{10mn^{3}}$$

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

$$\frac{5n}{4}\times \frac{2m}{5n}$$

Multiply \frac{5n}{4} times \frac{2m}{5n} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5n\times 2m}{4\times 5n}$$

Cancel out 2\times 5n in both numerator and denominator.

$$\frac{m}{2}$$