Question 160539
<pre><font size = 4 color = "indigo"><b>
{{{root(6,a^4)}}}

Use the definition rule:  {{{root(N,X^M)=X^(M/N)}}}

{{{root(6,a^4)=a^(4/6)}}}

But then we can reduce the fraction exponent {{{4/6}}} to {{{2/3}}}

{{{root(6,a^4)=a^(4/6)=a^(2/3)}}}

Now use the above definition rule in reverse {{{X^(M/N)=root(N,X^M)}}}
to get it back to a radical:

{{{root(6,a^4)=a^(4/6)=a^(2/3)=root(3,a^2)}}}

Edwin</pre>