Question
Find the value of :${\left\{ {{{\left( {\frac{{ - 2}}{3}} \right)}^{ - 2}}} \right\}^2}$
✓
Answer
${\left\{ {{{\left( {\frac{{ - 2}}{3}} \right)}^{ - 2}}} \right\}^2}$
$ = {\left( {\frac{{ - 2}}{3}} \right)^{( - 2) \times 2}}$
$ = {\left( {\frac{{ - 2}}{3}} \right)^{ - 4}}$
$ = \frac{{{{( - 2)}^{ - 4}}}}{{{{(3)}^{ - 4}}}}$
$ = \frac{{{3^4}}}{{{{( - 2)}^4}}}$
$ = \frac{{3 \times 3 \times 3 \times 3}}{{( - 2) \times ( - 2) \times ( - 2) \times ( - 2)}}$
$ = \frac{{81}}{{16}}$
$ = {\left( {\frac{{ - 2}}{3}} \right)^{( - 2) \times 2}}$
$ = {\left( {\frac{{ - 2}}{3}} \right)^{ - 4}}$
$ = \frac{{{{( - 2)}^{ - 4}}}}{{{{(3)}^{ - 4}}}}$
$ = \frac{{{3^4}}}{{{{( - 2)}^4}}}$
$ = \frac{{3 \times 3 \times 3 \times 3}}{{( - 2) \times ( - 2) \times ( - 2) \times ( - 2)}}$
$ = \frac{{81}}{{16}}$
= $5{1\over16}$
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