InterviewSolution
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InterviewSolution
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Express each of the following as a rational number of the form \(\frac{q}{p}\), where p and q are integers and q ≠ 0:(i) \(2^{-3}\)(ii) \((-4)^{-2}\)(iii) \(\frac{1}{3^{-2}}\)(iv) \((\frac{1}{2})^{-5}\)(v) \((\frac{2}{3})^{-2}\) |
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Answer» (i) \(2^{-3}\) = \(\frac{1}{2^{8}}\) = \(\frac{1}{8}\)[Using \(a^{-n} = \frac{1}{a^{n}}\)] (ii) \((-4)^{-2}\) = \(\frac{1}{-4^{2}}\) = \(\frac{1}{(-4)\times (-4)}\) =\(\frac{1}{16}\)[Using \(a^{-n} = \frac{1}{a^{n}}\) ] (iii) \(\frac{1}{3^{-2}}\) = \(\frac{3\times 3}{1}\) = \(\frac{9}{1}\)[Using \(\frac{1}{a^{-n}}\) = \(a^{n}\)] (iv) \((\frac{1}{2})^{-5}\) = \(\frac{2^{5}}{1^{5}}\) = \(\frac{2^{5}}{1}\) = \(\frac{32}{1}\)[Using \(a^{-n}\) = \(\frac{1}{a^{n}}\)] (v) \((\frac{2}{3})^{-2}\) = \(\frac{3^{2}}{2^{2}}\) = \(\frac{9}{4}\)[Using \(a^{-n}\) = \(\frac{1}{a^{n}}\);\(a^{2}\) = \(a\times a\)] |
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