Question
Evaluate :${\left\{ {{{\left( {\frac{1}{3}} \right)}^{ - 1}} - {{\left( {\frac{1}{4}} \right)}^{ - 1}}} \right\}^{ - 1}}$
✓
Answer
${\left\{ {{{\left( {\frac{1}{3}} \right)}^{ - 1}} - {{\left( {\frac{1}{4}} \right)}^{ - 1}}} \right\}^{ - 1}}$
$ = {\left( {\frac{{{1^{ - 1}}}}{{{3^{ - 1}}}} - \frac{{{1^{ - 1}}}}{{{4^{ - 1}}}}} \right)^{ - 1}} = {\left( {\frac{{{3^1}}}{{{1^1}}} - \frac{{{4^1}}}{{{1^1}}}} \right)^{ - 1}}$
$ = {\left( {\frac{3}{1} - \frac{4}{1}} \right)^{ - 1}}$ $= (3 – 4)^{-1}$
$ = {( - 1)^{ - 1}} = \frac{1}{{{{( - 1)}^1}}}$
$ = \frac{1}{{( - 1)}} = - 1$
$ = {\left( {\frac{{{1^{ - 1}}}}{{{3^{ - 1}}}} - \frac{{{1^{ - 1}}}}{{{4^{ - 1}}}}} \right)^{ - 1}} = {\left( {\frac{{{3^1}}}{{{1^1}}} - \frac{{{4^1}}}{{{1^1}}}} \right)^{ - 1}}$
$ = {\left( {\frac{3}{1} - \frac{4}{1}} \right)^{ - 1}}$ $= (3 – 4)^{-1}$
$ = {( - 1)^{ - 1}} = \frac{1}{{{{( - 1)}^1}}}$
$ = \frac{1}{{( - 1)}} = - 1$
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