The reciprocal of $( \frac{5}{7})^{-1}$ is:-
$( i).\ \frac{5}{7}$
$( ii).\ \frac{-5}{7}$
$( iii).\ \frac{7}{5}$
$( iv).\ \frac{-7}{5}$

Given: Fraction: $( \frac{5}{7})^{-1}$.

To do: To find the reciprocal of $( \frac{5}{7})^{-1}$.

Solution:

As known, reciprocal of $a=a^{-1}$

Therefore, reciprocal of $( \frac{5}{7})^{-1}=( ( \frac{5}{7})^{-1})^{-1}$

$=( \frac{5}{7})^{( -1)\times( -1)}$                   [$\because ( a^m)^n=a^{m\times n}$]

$=( \frac{5}{7})^{1}$

$=( \frac{5}{7})$

Thus, option $( i)$ is correct.

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Updated on: 10-Oct-2022

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