Simplify the following:
(0.027)−13(0.027)^{-\dfrac{1}{3}}(0.027)−31
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Given,
⇒(0.027)−13=[(0.3)3]−13=(0.3)−1=10.3=103=313.\Rightarrow (0.027)^{-\dfrac{1}{3}} = [(0.3)^3]^{-\dfrac{1}{3}} \\[1em] = (0.3)^{-1} = \dfrac{1}{0.3} \\[1em] = \dfrac{10}{3} = 3\dfrac{1}{3}. \\[1em]⇒(0.027)−31=[(0.3)3]−31=(0.3)−1=0.31=310=331.
Hence,(0.027)−13=313(0.027)^{-\dfrac{1}{3}} = 3\dfrac{1}{3}(0.027)−31=331.
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