Solve 8x^3y/27xy^3div16x^3y/45y

$$\frac { 8 x ^ { 3 } y } { 27 x y ^ { 3 } } \div \frac { 16 x ^ { 3 } y } { 45 y }$$

Evaluate

$$\frac{5}{6xy^{2}}$$

Solution Steps

Divide \frac{8x^{3}y}{27xy^{3}} by \frac{16x^{3}y}{45y} by multiplying \frac{8x^{3}y}{27xy^{3}} by the reciprocal of \frac{16x^{3}y}{45y}.

$$\frac{8x^{3}y\times 45y}{27xy^{3}\times 16x^{3}y}$$

Cancel out 8\times 9xyyx^{2} in both numerator and denominator.

$$\frac{5}{2\times 3xyy}$$

Multiply y and y to get y^{2}.

$$\frac{5}{2\times 3xy^{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{5}{6xy^{2}}$$

Differentiate w.r.t. x

$$-\frac{5}{6\left(xy\right)^{2}}$$