Question

By what number should \(5^{-1}\) be multiplied so that the product may be equal to \((-7)^{-1}\) ?

Answer 1

Let the number should \(5^{-1}\) be multiplied by x

According to the question:

\(x\times 5^{-1}=(-7)^{-1}\)

\(x\times \frac{1}{5}=\frac{1}{-7}\)[Using \(a^{-n}=\frac{1}{a^{n}}\)]

\(x=\frac{1}{-7}\div \frac{5}{1}=\frac{5}{-7}\)

\(x=\frac{1}{-7}\times \frac{5}{1}=\frac{5}{-7}\)= \(-\frac{5}{7}\)[Using and \(\frac{1}{a}\div \frac{1}{b}=\frac{1}{a}\times \frac{b}{1}\)]

Therefore \(5^{-1}\) should be multiplied by \(\frac{-5}{7}\)