Question 255880
Suppose we are given
{{{sqrt(a/b)}}}
the rules allow you to separate to get
{{{sqrt(a)/sqrt(b)}}}
Or as fractional exponents, we can say
{{{(a/b)^(x/y)}}}.
From here you can reduce a/b if appropriate or apply the powers.
EX: {{{sqrt(8/27)}}}
since you can't reduce the terms, split them apart as
{{{(sqrt(8))/(sqrt(27))}}}
and then simplify to get
{{{2sqrt(2)/(3sqrt(3))}}}
rationalizing the denominator gets us
{{{2sqrt(6)/3}}}
--
ex: {{{(sqrt(8/27))^3}}}
taking square roots first, we get
{{{(2sqrt(2)/3sqrt(3))^3}}}
second, apply the cube power to get
{{{(8*2sqrt(2))/(27*3sqrt(3))}}}
which is
{{{(16/81)*(sqrt(2)/sqrt(3))}}}
rationalized, it is
{{{16sqrt(6)/243}}}