Question

5. Express the following products as powers. Indicate the base and index in each case.
(i) a*a*a*a
(ii) x*x*x*x
(iii) b*b*b*b*b


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Answer 1

Answer:

Indices provide a compact algebraic notation for repeated multiplication. For example, is it much easier to write 35 than 3 × 3 × 3 × 3 × 3.

Once index notation is introduced the index laws arise naturally when simplifying numerical and algebraic expressions. Thus the simplificiation 25 × 23 = 28 quickly leads

to the rule am × an = am + n, for all positive integers m and n.

As often happens in mathematics, it is natural to ask questions such as