Simplify and express as positive indices:
[125a−3y6]−13\Big[\dfrac{125a^{-3}}{y^6}\Big]^{\dfrac{-1}{3}}[y6125a−3]3−1
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[125a−3y6]−13=[53a−3y6]−13=[5a−1y2]3×−13=[5a−1y2]−1=[y25a−1]1=[ay25]\Big[\dfrac{125a^{-3}}{y^6}\Big]^{\dfrac{-1}{3}}\\[1em] = \Big[\dfrac{5^{3}a^{-3}}{y^6}\Big]^{\dfrac{-1}{3}}\\[1em] = \Big[\dfrac{5a^{-1}}{y^2}\Big]^{3\times\dfrac{-1}{3}}\\[1em] = \Big[\dfrac{5a^{-1}}{y^2}\Big]^{-1}\\[1em] = \Big[\dfrac{y^2}{5a^{-1}}\Big]^{1}\\[1em] = \Big[\dfrac{ay^2}{5}\Big][y6125a−3]3−1=[y653a−3]3−1=[y25a−1]3×3−1=[y25a−1]−1=[5a−1y2]1=[5ay2]
[125a−3y6]−13=ay25\Big[\dfrac{125a^{-3}}{y^6}\Big]^{\dfrac{-1}{3}} = \dfrac{ay^2}{5}[y6125a−3]3−1=5ay2
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