question_answer 8)

                Evaluate:                 (i) \[{{3}^{-2}}\]                                (ii) \[{{(-4)}^{-2}}\]                          (iii) \[{{\left( \frac{1}{2} \right)}^{-5}}\]

Answer:

                (i) \[{{(3)}^{-2}}\] \[{{(3)}^{-2}}=\frac{1}{{{3}^{2}}}\,=\frac{1}{9}\] (ii) \[{{(-4)}^{-2}}\] \[{{(-4)}^{-2}}=\frac{1}{{{(-4)}^{2}}}=\frac{1}{16}\]                 (iii) \[{{\left( \frac{1}{2} \right)}^{-5}}\] \[{{\left( \frac{1}{2} \right)}^{-5}}\]\[=\frac{1}{{{\left( \frac{1}{2} \right)}^{5}}}\]                 \[=\frac{1}{\frac{{{1}^{5}}}{{{2}^{5}}}}\] \[=\frac{1}{\left( \frac{1}{32} \right)}\] = 32