Solve 50x^4/2y^5div625x^2/10y^3

$$\frac { 50 x ^ { 4 } } { 2 y ^ { 5 } } \div \frac { 625 x ^ { 2 } } { 10 y ^ { 3 } }$$

Evaluate

$$\frac{2\times \left(\frac{x}{y}\right)^{2}}{5}$$

Solution Steps

Divide \frac{50x^{4}}{2y^{5}} by \frac{625x^{2}}{10y^{3}} by multiplying \frac{50x^{4}}{2y^{5}} by the reciprocal of \frac{625x^{2}}{10y^{3}}.

$$\frac{50x^{4}\times 10y^{3}}{2y^{5}\times 625x^{2}}$$

Cancel out 2\times 5\times 25x^{2}y^{3} in both numerator and denominator.

$$\frac{2x^{2}}{5y^{2}}$$

Differentiate w.r.t. x

$$\frac{4x}{5y^{2}}$$