Powers

A power is a number multiplied by itself one or more times.

The base is the number being multiplied in a power and the index is how many times that number is multiplied together.

Example:         3⁴  = 3 · 3 · 3 · 3 = 81
''Three raised to the fourth power'', or ''3 to the fourth'' or ''the fourth power of 3'', equals eighty- one.

When the index is two, we say ''squared'', when it is three we say ''cubed'', when it is four we say ''to the fourth'', and so on.

Note: When we write 3⁴ we call it ''short way'' and when we write 3 · 3 · 3 · 3 we call it ''long way''.

Exercises:

1.- Write these powers the short way, using base and index, and calculate them:
a) 5·5·5 =                 b) 2·2·2·2·2·2 =        c) 10·10 =

2.- Write these powers the long way and calculate them:
a) 2⁷ =       b) 5 to the fourth =    c) 20 squared = 

Solutions:

1.- a) 5³ = 125; b) 2⁶ = 64; c) 10² = 100

2.- a) 2·2·2·2·2·2·2 = 128; b) 5·5·5·5 = 625; c) 20·20 = 400

3.- a) 3⁴ = 81; b) x·x·x·x·x; c) 2⁴ = 4·4 = 16 

4.- a) 2;5;32; b) 2;9; c) 4;3;64; d) 10;10.000

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