# 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 =

3.-
Fill the gaps

a) 3·3·3·3 = 4 =

b) = x5

c) 2·2·2·2 = 4 = = 42 =

4.-
Complete the table
 power base exponent value 25 JXUwMDZh JXUwMDZk JXUwMDZiJXUwMDAx 32 3 JXUwMDZh JXUwMDYx 43 JXUwMDZj JXUwMDZi JXUwMDZlJXUwMDAy 104 JXUwMDY5JXUwMDAx 4 JXUwMDY5JXUwMDAxJXUwMDFlJXUwMDFlJXUwMDAwJXUwMDAw

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

In the end, you can go to this site and play for a while: http://www.ezschool.com/Games/Exponents.html

Licensed under the Creative Commons Attribution Non-commercial Share Alike 3.0 License