Pre Algebra Exponents
Math-Prof HOME Pre Algebra Table of Contents Ask A Question PREV NEXT

Fancy Multiplying
Exponents

 
 Sometimes we need to multiply a number times itself, like:
 

 2 2 = 4

 
 And sometimes we need to multiply the number times itself a bunch of times:
 

 2 2 2 2 2 = 32

 
 If we multiply a bunch of a number it gets easy to make a mistake. 
 Math people wanted an quick way to write these down these problems.
 They came up with a way that uses very little space 
 no matter how big the problem is.
 
 What they do is write the number once. 
 Then they write down how many times the number gets multiplied. 
 So everybody knows which number means what. 
 It gets written like this:
 

 

 

 25 means 2 2 2 2 2

 
 The little number 5 up in the air is called an exponent. 
 In math talk, that means how many times you multiply the number times itself.
 
 There's an easy mistake you can make 
 when you start to work with these exponent things. 
 
 That is to try to multiply the exponent. 
 To see this problem as 2 x 5.
 

NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! NO! 

 
 The exponent just tells you what to do. 
 It says:
 Multiply the number to my left, TIMES ITSELF this many times.
 
 So:
 
  21 = 2
 
  24 = 2 2 2 2 = 16
 
  210 = 2 2 2 2 2 2 2 2 2 2 = 1024
 
 WOW! exponents are really POWERFUL. 
 Take a 2 and a 10 and BINGO. You've got 1024! 
 Because of this, exponents are sometimes called powers. 
 
 If you have:
 

 36

 
 You would say "3 raised to the sixth power" 
 or just "3 to the sixth power" for short. 
 (Even 3 to the sixth for mega short)
 
 Pop Quiz: 
 Does 3 6 mean 3 6?
 

 NOT A CHANCE!

 
 It means:
 

 3 3 3 3 3 3 = 729

 
 The bad news is that there's no easy way to multiply six 3's together. 
 You multiply the first 2: 3 x 3 = 9. 
 Then multiply that by the third 3: 9 x 3 = 27
 and so on.
 
 If you have a nice calculator, it might have a key like this:
 

 

 
 If it does, try getting the answer to 3 6 using these key punches:
 

 

 
 If that doesn't make the calculator come back with 729, 
 check the instructions
 
 Some calculators (especially some made by Hewlett Packard) 
 use a different key order.
 
 OK, Review time:
 
  23 = 2 2 2 = 8
 
  54 = 5 5 5 5 = 625
 
  15 = 1 1 1 1 1 = 1
 
  02 = 0 0 = 0
 

   copyright 2005 Bruce Kirkpatrick

Math-Prof HOME Pre Algebra Table of Contents Ask A Question PREV NEXT