Simplify:
(27x−3y6)23(27x^{-3}y^6)^{\dfrac{2}{3}}(27x−3y6)32
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(27x−3y6)23=(27y6x3)23=(33y2×3x3)23=(3y2x)3×23=(3y2x)63=(3y2x)2=9y4x2=9y4x−2(27x^{-3}y^6)^{\dfrac{2}{3}}\\[1em] = \Big(\dfrac{27y^6}{x^3}\Big)^{\dfrac{2}{3}}\\[1em] = \Big(\dfrac{3^3y^{2\times3}}{x^3}\Big)^{\dfrac{2}{3}}\\[1em] = \Big(\dfrac{3y^2}{x}\Big)^{3\times\dfrac{2}{3}}\\[1em] = \Big(\dfrac{3y^2}{x}\Big)^{\dfrac{6}{3}}\\[1em] = \Big(\dfrac{3y^2}{x}\Big)^2\\[1em] = \dfrac{9y^4}{x^2}\\[1em] = 9y^4x^{-2}(27x−3y6)32=(x327y6)32=(x333y2×3)32=(x3y2)3×32=(x3y2)36=(x3y2)2=x29y4=9y4x−2
(27x−3y6)23=9y4x−2(27x^{-3}y^6)^{\dfrac{2}{3}} = 9y^4x^{-2}(27x−3y6)32=9y4x−2
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