Question 50653
Okay, if it is a fourth root, then you need to recognize that 81 is a perfect 4th power, that is {{{3^4 = 81}}} so {{{root(4, 81)=3}}}.  Also, you need to know that if you have a variable raised to a power, then you divide the exponents by 4.  The problem here is that the exponent of x is 6 which is NOT divisible by 4.  So you have to break it down and write {{{x^6= x^4*x^2}}}.


{{{root(4, 81x^6*y^8) }}}

{{{root(4, 81x^4*y^8) *root(4, x^2)}}}
{{{ 3xy^2* root(4, x^2)}}}


Now, there is an additional problem, that the {{{root(4,x^2)}}} reduces to {{{sqrt(x) }}}.  This is called reducing the order of a radical, which to my way of thinking is a College Algebra skills.  Have you had anything like that??


So the last step becomes this:
{{{ 3xy^2* root(4, x^2)}}}

{{{ 3xy^2* sqrt( x)}}}



R^2 at SCC