Solve (x^2y^6/x^3)(frac{x^7{y}^9}{{x}^2{y}^6})

$$( \frac{ { x }^{ 2 } { y }^{ 6 } }{ { x }^{ 3 } } )( \frac{ { x }^{ 7 } { y }^{ 9 } }{ { x }^{ 2 } { y }^{ 6 } } )$$

Evaluate

$$x^{4}y^{9}$$

Solution Steps

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

$$\frac{y^{6}}{x}\times \frac{x^{7}y^{9}}{x^{2}y^{6}}$$

Cancel out x^{2}y^{6} in both numerator and denominator.

$$\frac{y^{6}}{x}y^{3}x^{5}$$

Express \frac{y^{6}}{x}y^{3} as a single fraction.

$$\frac{y^{6}y^{3}}{x}x^{5}$$

Express \frac{y^{6}y^{3}}{x}x^{5} as a single fraction.

$$\frac{y^{6}y^{3}x^{5}}{x}$$

Cancel out x in both numerator and denominator.

$$y^{3}x^{4}y^{6}$$

To multiply powers of the same base, add their exponents. Add 3 and 6 to get 9.

$$y^{9}x^{4}$$

Differentiate w.r.t. x

$$4x^{3}y^{9}$$