Solve {l}{2(-a^{3})^{6}-3(-a^{2}*a^{4})^{3}+a^{18}-4a^{2}}{(-a^2)^2*(-a^3)^4}

$$\left. \begin{array} { l } { 2 ( - a ^ { 3 } ) ^ { 6 } - 3 ( - a ^ { 2 } \cdot a ^ { 4 } ) ^ { 3 } + a ^ { 18 } - 4 a ^ { 2 } } \\ { ( - a ^ { 2 } ) ^ { 2 } \cdot ( - a ^ { 3 } ) ^ { 4 } } \end{array} \right.$$

Least Common Multiple

$$6a^{32}-4a^{16}$$

Solution Steps

Factor the expressions that are not already factored.

$$-4a^{2}+6a^{18}=2a^{2}\left(3a^{16}-2\right)$$

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

$$2a^{16}\left(3a^{16}-2\right)$$

Expand the expression.

$$6a^{32}-4a^{16}$$

Evaluate

$$6a^{18}-4a^{2},\ a^{16}$$