



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: 











2^{5} 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: 






2^{1}
=
2 







2^{4}
= 2 ×
2 ×
2 ×
2 =
16 







2^{10}
= 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: 





3^{6}






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: 






2^{3}
= 2 ×
2 ×
2 =
8 







5^{4}
= 5 ×
5 ×
5 ×
5 =
625 







1^{5}
= 1 ×
1 ×
1 ×
1 ×
1 = 1 







0^{2}
= 0 ×
0 =
0 





copyright 2005 Bruce Kirkpatrick 
