Question 421869
m^(2/3) = {{{(root(3,m))^2}}} or {{{root(3,m^2)}}}


m^(2/3) is equivalent to (m^(1/3))^2.


m^(2/3) is also equivalent to( m^2)^(1/3)


the exponentiation rule that makes this happen is (m^a)^b = m^(a*b).


this allows (m^(1/3))^2 to be equal to m^(2/3).


this also allows (m^2)^(1/3) to be equal to m^(2/3).


this is because 2 * (1/3) = 2/3 and (1/3) * 2  = 2/3.


any time you have x^(1/n), you can replace it with {{{root(n,x)}}}


any time you have x^(y/n), you can replace it with (x^y)^(1/n) or you can replace it with (x^(1/n)^y.


if with (x^y)^(1/n), then it becomes {{{root(n,(x^y))}}}


if with (x^(1/n))^y, then it becomes {{{(root(n,x))^y}}}