Negative Indices

Negative Indices

Secondary 3

Evaluate the following, without the use of a calculator.

  1. \({{5}^{-3}}\)
  1. \({{\left( \frac{1}{7} \right)}^{-1}}\)

  1. \({{\left( -3 \right)}^{-2}}\)
  1. \({{2}^{0}}+{{2}^{-3}}\)
  1. \({{\left( \frac{2}{3} \right)}^{-3}}\)
  1. \({{\left( {{2}^{-2}} \right)}^{3}}\times {{\left( {{2}^{-3}} \right)}^{-2}}\)

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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Finding similar questions...
Answer:(i) \(\frac{1}{125}\). (ii) \(\frac19\). (iii) \(3\frac38\). (iv) \(7\). (v) \(1\frac18\). (vi) \(1\).

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