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Express each of the following rational numbers with a negative exponent:(i) \((\frac{1}{4})^{3}\)(ii) \(3^{5}\)(iii) \((\frac{3}{5})^{4}\)(iv) \(\{(\frac{3}{2})^{4}\}^{-3}\)(v) \(\{(\frac{7}{3})^{4}\}^{-3}\) |
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Answer» (i) \((\frac{1}{4})^{3}\) ⇒ \((\frac{1}{4})^{3}\)= \((4)^{-3}\)[Using \(\frac{1}{a^{n}}\)= \(a^{-n}\)] (ii) \(3^{5}\) ⇒ \(3^{5}\)= \((\frac{1}{3})^{-5}\)= \((4)^{-3}\)[Using \(\frac{1}{a^{n}}\)= \(a^{-n}\)] (iii) \((\frac{3}{5})^{4}\) ⇒ \((\frac{3}{5})^{4}\)= \((\frac{5}{3})^{-4}\)[Using \((\frac{a}{b})^{-n}\)= \((\frac{b}{n})^{n}\)] (iv) \(\{(\frac{3}{2})^{4}\}^{-3}\) ⇒ \(\{(\frac{3}{2})^{4}\}^{-3}\) = \((\frac{3}{2})^{-12}\)[Using (aⁿ)ᵐ = aᵐⁿ] (v) \(\{(\frac{7}{3})^{4}\}^{-3}\) ⇒ \(\{(\frac{7}{3})^{4}\}^{-3}\)= \((\frac{7}{3})^{-12}\)[Using (aⁿ)ᵐ = aᵐⁿ] |
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