First, eliminate the outer exponent of the term on the right of the expression using these rules of exponents:
#a = a^color(red)(1)# and #(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))#
#(-2x^2y^4z^3)(-3^color(red)(1)x^color(red)(1)y^2z^color(red)(1))^color(blue)(2) =>#
#(-2x^2y^4z^3)(-3^(color(red)(1)xxcolor(blue)(2))x^(color(red)(1)xxcolor(blue)(2))y^(2xxcolor(blue)(2))z^(color(red)(1)xxcolor(blue)(2))) =>#
#(-2x^2y^4z^3)(-3^2x^2y^4z^2) =>#
#(-2x^2y^4z^3)(9x^2y^4z^2)#
Next, rewrite this expression as:
#(-2 xx 9)(x^2 xx x^2)(y^4 xx y^4)(z^3 xx z^2) =>#
#-18(x^2 xx x^2)(y^4 xx y^4)(z^3 xx z^2)#
Now, use this rule of exponents to complete the multiplication:
#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#
#-18(x^color(red)(2) xx x^color(blue)(2))(y^color(red)(4) xx y^color(blue)(4))(z^color(red)(3) xx z^color(blue)(2)) => -18x^(color(red)(2) + color(blue)(2))y^(color(red)(4) + color(blue)(4))z^(color(red)(3) + color(blue)(2)) =>#
#-18x^4y^8z^5#
