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### 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.

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
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

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

Good question; thanks for writing.

-Doctor Mike,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

Associated Topics:
Middle School Square Roots

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