Solve {l}{9x^{3}y^{3}*(-1/3x^{2}y)^{2}+(-x^{2}y)^{3}x}{x*(-x^2)^3*(x^3)^2}

$$\left. \begin{array} { l } { 9 x ^ { 3 } y ^ { 3 } \cdot ( - \frac { 1 } { 3 } x ^ { 2 } y ) ^ { 2 } + ( - x ^ { 2 } y ) ^ { 3 } x } \\ { x \cdot ( - x ^ { 2 } ) ^ { 3 } \cdot ( x ^ { 3 } ) ^ { 2 } } \end{array} \right.$$

Least Common Multiple

$$\left(y^{2}-1\right)y^{3}x^{13}$$

Solution Steps

Factor the expressions that are not already factored.

$$x^{7}y^{3}\left(y^{2}-1\right)=\left(y-1\right)\left(y+1\right)y^{3}x^{7}$$

Identify all the factors and their highest power in all expressions. Multiply the highest powers of these factors to get the least common multiple.

$$\left(y-1\right)\left(y+1\right)y^{3}x^{13}$$

Expand the expression.

$$y^{5}x^{13}-y^{3}x^{13}$$

Evaluate

$$\left(y^{2}-1\right)y^{3}x^{7},\ -x^{13}$$