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Inverse of Rational Numbers

Find the reci...

Question

Find the reciprocal of the rational number $(\frac{1}{3}) + {(\frac{4}{5})}^{- 3}$

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Solution

$(\frac{1}{3}) \times {(\frac{4}{5})}^{- 3}$ $= \frac{1}{3} \times {(\frac{5}{4})}^{3}$
$= \frac{1}{3} \times \frac{125}{64}$
$= \frac{125}{192}$
Therefore, the reciprocal is $\frac{192}{125}$

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