Solve frac{2y^{9}x^{5}}{5x^2}*125xy^5/16x^4y^10

$$\frac { 2 y ^ { 9 } x ^ { 5 } } { 5 x ^ { 2 } } \times \frac { 125 x y ^ { 5 } } { 16 x ^ { 4 } y ^ { 10 } }$$

Evaluate

$$\frac{25y^{4}}{8}$$

Solution Steps

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

$$\frac{2x^{3}y^{9}}{5}\times \frac{125xy^{5}}{16x^{4}y^{10}}$$

Cancel out xy^{5} in both numerator and denominator.

$$\frac{2x^{3}y^{9}}{5}\times \frac{125}{16x^{3}y^{5}}$$

Multiply \frac{2x^{3}y^{9}}{5} times \frac{125}{16x^{3}y^{5}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2x^{3}y^{9}\times 125}{5\times 16x^{3}y^{5}}$$

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

$$\frac{25y^{4}}{8}$$

Differentiate w.r.t. y

$$\frac{25y^{3}}{2}$$