As you know, exponents can be
positive numbers, negative numbers, or zero.
Let's take a closer look at how to deal with exponents. 

Remember the rule for dividing
like variables raised to a power?

Obviously,
these answers are
the same !!!!!

Negative exponent rule:
(Remember that x cannot equal 0
or a division by zero error will occur.) 

Example:


Remember:
an
expression with a negative power ends up on the
opposite side
of the fraction bar as a positive power. 


A Zero
exponent is investigated
in much the same way.



If we subtract the exponents, we get: 

If we cancel, we get: 



Also EQUAL
Answers!!!!



So,
,
as long as
. 

(The above rule is based on division. Since we cannot divide by a zero
quantity,
we must add the condition that
.)

In problems dealing with negative
and zero exponents,
simplify whenever possible by using the rules stated above.
Check out the following problems: 

Example 1.

Solution:
(Remember, anything to the '0' power has a value of
'1'.
Notice that the power of 0 affects the entire parentheses which is
raised to that power.)

Example 2.

Solution:
(In this problem, we have used negative powers to
move
the y variable to the numerator
and to combine the x values.
This is not the only way to express the answer.)

Example 3.

Solution:
(The 2 raised to the negative power moves to the
numerator
with a positive power.
Notice that the 0 power only affects the 4 which is raised to that
power.
It does not affect the multiple of 4.) 
Example 4.

Solution:
(Notice how the parentheses affects the power of 3. If the power
is outside the parentheses, all of the elements within the parentheses
are affected, as in the first part of the problem. If there are no
parentheses, as in the last part of the problem, the power affects only
the term to which it is assigned (attached).)

Example 5.

Solution:
(When solving these problems, it is usually easier to simplify inside the parentheses first.
Then
deal with the outside exponent. Did you notice that the last step
shows the negative
powers expressed as positive powers on the opposite side of the fraction
bar?)

