Opposite of an Exponent

Date: 05/18/97 at 13:19:55
From: Rebecca Carter
Subject: Algebra - Exponents

How do you solve an equation like this: a^2 = 36?

I have tried to solve this, but exponents don't have an opposite (like
the opposite of + is -), so I am not sure how you solve this.  

Thank you for your help!

Yours truly,
Rebecca Carter

Date: 05/18/97 at 23:25:33
From: Doctor Mike
Subject: Re: Algebra - Exponents

Dear Rebecca,
  
The word opposite is a pretty good choice for the relation between 
addition and subtraction.  If you start with a certain number, add 5 
and then subtract 5, you get back where you started.  Notice that "5 
minus 5" is zero, which is a very special number for addition.  You 
can add zero to any other number without changing it. Zero is the 
"identity" for addition.
   
There is a similar relationship between multiplication and division.  
If you start with a certain number, multiply it by 5 and then divide 
by 5, you get back where you started. Notice that "5 divided by 5" is 
one, which is a very special number for multiplication.  You can 
multiply any number by one without changing it.  One is the "identity" 
for multiplication. 
  
The opposite of squaring something is taking the square root. The 
opposite of cubing something is taking the cube root, etc. So, if you 
have an equation like the one above, you could take the square root of 
both sides to get a=6.  You do need to be CAREFUL whenever you do 
this, to remember that a number has 2 square roots.  The square of 6 
is 36, but the square of -6 is also 36.  So, the equation you ask 
about has TWO different answers.  

Good question; thanks for writing.  
  
-Doctor Mike,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/