Solve (-3/2ax^{4}y^3)div(-6/5ax^2y^2)*8a^2y

$$( - \frac { 3 } { 2 } a x ^ { 4 } y ^ { 3 } ) \div ( - \frac { 6 } { 5 } a x ^ { 2 } y ^ { 2 } ) \cdot 8 a ^ { 2 } y$$

Evaluate

$$10\left(axy\right)^{2}$$

Solution Steps

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

$$\frac{-\frac{3}{2}yx^{2}}{-\frac{6}{5}}\times 8a^{2}y$$

Divide -\frac{3}{2}yx^{2} by -\frac{6}{5} by multiplying -\frac{3}{2}yx^{2} by the reciprocal of -\frac{6}{5}.

$$\frac{-\frac{3}{2}yx^{2}\times 5}{-6}\times 8a^{2}y$$

Multiply -\frac{3}{2} and 5 to get -\frac{15}{2}.

$$\frac{-\frac{15}{2}yx^{2}}{-6}\times 8a^{2}y$$

Divide -\frac{15}{2}yx^{2} by -6 to get \frac{5}{4}yx^{2}.

$$\frac{5}{4}yx^{2}\times 8a^{2}y$$

Multiply \frac{5}{4} and 8 to get 10.

$$10yx^{2}a^{2}y$$

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

$$10y^{2}x^{2}a^{2}$$

Differentiate w.r.t. x

$$20x\left(ay\right)^{2}$$