Simplify the given expression, using only positive exponents. then complete the statements that follow. [ (x2y3)−1 (x−2y2z)2 ] 2 , x ≠ 0, y ≠ 0, z ≠ 0.
Accepted Solution
A:
Answer:[tex]x^{-12}y^{2}z^{4}[/tex]Step-by-step explanation:We have to simplify the given expression given as [tex][(x^{2}y^{3})^{-1}.(x^{-2}y^{2}z)^{2}]^{2}[/tex][tex][x^{-2}.y^{-3}.x^{-4}.y^{4}.z^{2}]^{2}[/tex][tex][x^{-2-4}.y^{-3+4}.z^{2}]^{2}=[x^{-6}.y^{1}.z^{2}]^{2}=x^{(-6-6)}.y^{1+1}.z^{2+2}=x^{-12}y^{2}z^{4}[/tex]Therefore simplification of the given expression gives [tex]x^{-12}y^{2}z^{4}[/tex]