Simplifying exponential functions

Question

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.  

Answer 1

Hello John,

 

You are correct that y⁰ and that x^1/2=√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/x^1/2

=x^2-1/2

=x^3/2

 

So we end up with the final answer of -x^3/2y²

 

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