Question 536248
{{{root(4, 27y^3)/root(4, 8x^7)}}}  

<P>
To rationalize the denominator, multiply by 1 in the form of denominator/denominator.  Any number over itself is 1, and 1 times anything is the thing itself.<P>
{{{root(4, 27y^3)/root(4, 8x^7)*root(4, 8x^7)/root(4, 8x^7)=root(4, 216x^7y^3)/8x^7}}}  <P>
Anything that's raised to the 4th power can be pulled out of the 4th root.  <P>
{{{x^7=x^4x^3}}}  So it becomes  {{{root(4, 216x^4x^3y^3)/8x^7 = x*root(4, 216x^3y^3)/8x^7}}}<P>
{{{x}}} cancels with {{{x^7}}} to leave {{{x^6}}} on the bottom.<P>
{{{root(4,216x^3y^3)/8x^6}}}
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