Question

Which of the following is equivalent to [ (x^ 2 y^ 3 )^ -2/ (x^ 6 y^ 3 z)^3]? worth 60 points!

Answer 1

Answer:

$\displaystyle \frac{1}{x^{48}y^{36}z^6}$

Step-by-step explanation:

$\displaystyle[\frac{(x^2 y^3)^{-2}}{(x^6 y^3 z)^2 } ]^3$

$\displaystyle \frac{(x^2 y^3)^{-6}}{(x^6 y^3 z)^6 }$

$\displaystyle \frac{(x^{-12} y^{-18})}{(x^{36} y^{18}z^6 ) }$

$\displaystyle \frac{x^{-48} y^{-36}}{z^6 }$

$\displaystyle \frac{1}{x^{48}y^{36}z^6}$

Answer 2

Answer:

$\dfrac{1}{x^{48}y^{36}z^{6}}$

Step-by-step explanation:

$(\dfrac{(x^2y^3)^{-2}}{(x^6y^3z)^{2}})^3 =$

$= (\dfrac{1}{(x^6y^3z)^{2}(x^2y^3)^{2}})^3$

$= (\dfrac{1}{x^{12}y^6z^{2}x^4y^6})^3$

$= (\dfrac{1}{x^{16}y^{12}z^{2}})^3$

$= \dfrac{1}{x^{48}y^{36}z^{6}}$