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Simplifying exponential functions

Need to simplify:
 
-x²y²
x½y0

I know that y0= 1 and x½ = √x

which leaves me with -x²y²
                                     √x
 
But then I am stuck.  
Thanks for helping.  
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1 Answer

Hello John,
 
You are correct that y0 and that x1/2=√x.  However, in this type of problem, it is best not to convert to a square root at this step. Instead, beginning from this point:
 
(-x²y²)/(x½)
 
The rule is that if you are dividing a variable, we subtract the values for their exponents.  This means that:
x2/x1/2
=x2-1/2
=x3/2
 
So we end up with the final answer of -x3/2y2
 
This form is generally considered the most simplified form, but if you want to express it with the square root, you can also call it:
 
-√(x3)y2

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