Simplify and express as positive indices:
[32x−5243y−5]−15\Big[\dfrac{32x^{-5}}{243y^{-5}}\Big]^{\dfrac{-1}{5}}[243y−532x−5]5−1
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[32x−5243y−5]−15=[25x−535y−5]−15=[2x−13y−1]5×−15=[2x−13y−1]−1=[2y3x]−1=[3x2y]\Big[\dfrac{32x^{-5}}{243y^{-5}}\Big]^{\dfrac{-1}{5}}\\[1em] = \Big[\dfrac{2^{5}x^{-5}}{3^5y^{-5}}\Big]^{\dfrac{-1}{5}}\\[1em] = \Big[\dfrac{2x^{-1}}{3y^{-1}}\Big]^{5\times\dfrac{-1}{5}}\\[1em] = \Big[\dfrac{2x^{-1}}{3y^{-1}}\Big]^{-1}\\[1em] = \Big[\dfrac{2y}{3x}\Big]^{-1}\\[1em] = \Big[\dfrac{3x}{2y}\Big][243y−532x−5]5−1=[35y−525x−5]5−1=[3y−12x−1]5×5−1=[3y−12x−1]−1=[3x2y]−1=[2y3x]
[32x−5243y−5]−15=[3x2y]\Big[\dfrac{32x^{-5}}{243y^{-5}}\Big]^{\dfrac{-1}{5}}= \Big[\dfrac{3x}{2y}\Big][243y−532x−5]5−1=[2y3x]
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