Exponents
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Simplify each of the following as much as possible.
1. 
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All of these problems make use of
one or more of the following properties.
This particular problem only uses
the first property.
Remember that the y’s in the last two terms can’t be
combined! You can only combine terms
that are products or quotients. Also,
while this would be an acceptable and often preferable answer in a calculus
class an algebra class would probably want you to get rid of the negative
exponents as well. In this case your
answer would be.
The 2 will stay in the numerator
of the first term because it doesn’t have a negative exponent.
2.
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Not much to this solution other
than just adding the exponents.
3.
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Note that you could also have done
the following (probably is easier….).
In the second case I first
canceled an x before doing any
simplification.
In both cases the 2 stays in the
denominator. Had I wanted the 2 to come
up to the numerator with the x I
would have used in the denominator. So watch parenthesis!
4.
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There are a couple of ways to
proceed with this problem. I’m going to
first simplify the inside of the parenthesis a little. At the same time I’m going to use the last
property above to get rid of the minus sign on the whole thing.
Now bring the exponent in. Remember that every term (including the 2)
needs to get the exponent.
Recall that so you can’t go any further with this.
5.
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Don’t make this one harder than it
has to be. Note that the whole thing is
raised to the zero power so there is only one property that needs to be used
here.