Find the value of: (i) (5/8)^(-1) (ii) (-4/9)^(-1)

Question

Find the value of:

(i) \((\frac{5}{8})^{-1}\)

(ii) \((\frac{-4}{9})^{-1}\)

(iii) \((-7)^{-1}\)

(iv) \((\frac{1}{-3})^{-1}\)

Answer 1

Let there be a rational number \(\frac{a}{b}\) then \((\frac{a}{b})^{-1}\) = \(\frac{b}{a}\)

Therefore,

(i)

\((\frac{5}{8})^{-1}=\frac{8}{5}\)

(ii)

\((\frac{-4}{9})^{-1}=\frac{9}{-4} =\frac{9\times-1}{-4\times-1}=\frac{-9}{4}\)

(iii)

\((-7)^{-1}=(\frac{-7}{1})^{-1}=\frac{1}{-7}= \frac{1\times-1}{-7\times-1}=\frac{-1}{7}\)

(iv)

\((\frac{1}{-3})^{-1}=\frac{-3}{1}=-3\)