Question

find its reciprocal
$\frac{1}{3}^{ - 1} \div ( \frac{4}{5} ^{ - 3}$
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Answer 1

Given,

                the value $(\frac{1}{3} )^{-1}$ ÷ $(\frac{4}{5})^{-3}$

To find,

         To find the reciprocal of the given value.

Solution,

         To find the reciprocal of the given value, we should first simplify the value, and then reciprocal can be obtained by interchanging the numerator & denominator.

             $(\frac{1}{3}) ^{-1}$ = $((3)^{-1} )^{-1}$= 3       [ $\frac{1}{n}$ = $n^{-1}$ ]

And      $(\frac{4}{5})^{-3}$ = $(\frac{5}{4} )^{3}$ = $\frac{125}{64}$

Therefore,     $(\frac{1}{3} )^{-1}$ ÷ $(\frac{4}{5})^{-3}$ = 3 ÷ $\frac{125}{64}$

                                           = (3×64)/125 = 192 /125

    Since      $(\frac{1}{3} )^{-1}$ ÷ $(\frac{4}{5})^{-3}$ = 192/125

Therefore, the reciprocal of the given value is 125/192.