Solve {l}{text{(1)}x^{7}divx^{4}}{text{(2)}(-a)^{6}div(-a)^{3}}{text{(3)}(ab)^{4}div(ab)^{2}}{text{(4)}(2a+b)^{8}div(2a+b)^{5}}{text{(5)}(-3xy^{2})^{2}*2xydiv(3x^2y^5)}{text{(6)}(x-y)^5div(y-x)^3}

$$\left. \begin{array} { l } { \text { (1) } x ^ { 7 } \div x ^ { 4 } } \\ { \text { (2) } ( - a ) ^ { 6 } \div ( - a ) ^ { 3 } } \\ { \text { (3) } ( a b ) ^ { 4 } \div ( a b ) ^ { 2 } } \\ { \text { (4) } ( 2 a + b ) ^ { 8 } \div ( 2 a + b ) ^ { 5 } } \\ { \text { (5) } ( - 3 x y ^ { 2 } ) ^ { 2 } \cdot 2 x y \div ( 3 x ^ { 2 } y ^ { 5 } ) } \\ { \text { (6) } ( x - y ) ^ { 5 } \div ( y - x ) ^ { 3 } } \end{array} \right.$$

Least Common Multiple

$$60\left(b\left(x-y\right)\right)^{2}\left(ax\left(b+2a\right)\right)^{3}$$

Solution Steps

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

$$60b^{2}\left(x-y\right)^{2}a^{3}x^{3}\left(b+2a\right)^{3}$$

Expand the expression.

$$60a^{3}b^{5}x^{5}+360a^{4}b^{4}x^{5}+480b^{2}x^{5}a^{6}+720b^{3}a^{5}x^{5}+60y^{2}a^{3}x^{3}b^{5}+360y^{2}x^{3}a^{4}b^{4}+480b^{2}y^{2}x^{3}a^{6}+720y^{2}b^{3}x^{3}a^{5}-1440yb^{3}x^{4}a^{5}-960yb^{2}x^{4}a^{6}-720ya^{4}b^{4}x^{4}-120ya^{3}x^{4}b^{5}$$

Evaluate

$$x^{3},\ -2a^{3},\ 3\left(ab\right)^{2},\ 4\left(b+2a\right)^{3},\ 30x,\ -6\left(y-x\right)^{2}$$