Solve (frac{3x^{4}y^{5}}{6x^{6}y^{8}})(9x^7y^5/3x^3y^5)

$$( \frac { 3 x ^ { 4 } y ^ { 5 } } { 6 x ^ { 6 } y ^ { 8 } } ) ( \frac { 9 x ^ { 7 } y ^ { 5 } } { 3 x ^ { 3 } y ^ { 5 } } )$$

Evaluate

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

Solution Steps

Cancel out 3x^{4}y^{5} in both numerator and denominator.

$$\frac{1}{2x^{2}y^{3}}\times \frac{9x^{7}y^{5}}{3x^{3}y^{5}}$$

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

$$\frac{1}{2x^{2}y^{3}}\times 3x^{4}$$

Express \frac{1}{2x^{2}y^{3}}\times 3 as a single fraction.

$$\frac{3}{2x^{2}y^{3}}x^{4}$$

Express \frac{3}{2x^{2}y^{3}}x^{4} as a single fraction.

$$\frac{3x^{4}}{2x^{2}y^{3}}$$

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

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

Differentiate w.r.t. x

$$\frac{3x}{y^{3}}$$