Solve frac{x^{3}y^6}{x^4y^3}:x^7y=

$$\frac { x ^ { 3 } y ^ { 6 } } { x ^ { 4 } y ^ { 3 } } : x ^ { 7 } y =$$

Evaluate

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

Solution Steps

Express \frac{\frac{x^{3}y^{6}}{x^{4}y^{3}}}{x^{7}} as a single fraction.

$$\frac{x^{3}y^{6}}{x^{4}y^{3}x^{7}}y$$

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

$$\frac{y^{3}}{xx^{7}}y$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$\frac{y^{3}}{x^{8}}y$$

Express \frac{y^{3}}{x^{8}}y as a single fraction.

$$\frac{y^{3}y}{x^{8}}$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

Differentiate w.r.t. x

$$-\frac{8y^{4}}{x^{9}}$$