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By what number should \((\frac{5}{3})^{-2}\) be multiplied so that the product may be \((\frac{7}{3})^{-1}\)? |
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Answer» Let the number should \((\frac{5}{3})^{-2}\) be multiplied by x According to the question: \(x\times (\frac{5}{3})^{-2}\)= \((\frac{7}{3})^{-1}\) \(x\times (\frac{3}{5})^{2}\)= \(\frac{3}{7}\)[Using \(a^{-n}=\frac{1}{a^{n}}\)] \(x= \frac{3}{7}\div (\frac{3}{5})^{2}\) \(x=\frac{3}{7}\times \frac{25}{7}=\frac{25}{21}\)[Using and \(\frac{1}{a}\div \frac{1}{b}\)= \(\frac{1}{a}\times \frac{b}{1}\)] Therefore \((\frac{1}{2})^{-1}\) should be multiplied by \(\frac{25}{21}\) |
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