Question 48500
<pre><font size = 5><b>Simplify. Assume all variables represents positive 
numbers:
 ____
<font face = "symbol">Ö</font>x<sup>4</sup>y<sup>3</sup>

Prime factor everything under the radical:
 _______
<font face = "symbol">Ö</font>xxxxyyy

Since the index of the radical is understood to be 2,
group into twos, or pairs of like factors:
 _____________
<font face = "symbol">Ö</font>(xx)(xx)(yy)y

Now each pair of like factors can be written as a
square:
 _______
<font face = "symbol">Ö</font>x<sup>2</sup>x<sup>2</sup>y<sup>2</sup>y

Take each square out in front as the base without the
exponent, leaving the y that did not pair under the
radical:
    _
xxy<font face = "symbol">Ö</font>y

or
    _
x<sup>2</sup>y<font face = "symbol">Ö</font>y

Edwin</pre>