Negative Indices
Negative Indices
Secondary 3
Evaluate the following, without the use of a calculator.
- \({{5}^{-3}}\)
- \({{\left( \frac{1}{7} \right)}^{-1}}\)
- \({{\left( -3 \right)}^{-2}}\)
- \({{2}^{0}}+{{2}^{-3}}\)
- \({{\left( \frac{2}{3} \right)}^{-3}}\)
- \({{\left( {{2}^{-2}} \right)}^{3}}\times {{\left( {{2}^{-3}} \right)}^{-2}}\)
Important:
From Worked Example 1 (iii) and (iv), we can have the following result:
\({{\left( \frac{a}{b} \right)}^{-n}}={{\left( \frac{b}{a} \right)}^{n}}\)
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Answer:(i) \(\frac{1}{125}\). (ii) \(\frac19\). (iii) \(3\frac38\). (iv) \(7\). (v) \(1\frac18\). (vi) \(1\).
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