Question 707147
<pre>
The other tutor went into a lot of detail after she
got here.  

{{{ x = 1+root(3,16^4) }}}

Maybe you'd like this better:

Write the 16 as {{{2^4}}}

{{{ x = 1+root(3,(2^4)^4) }}}

Then multiply the two exponents 4·4 = 16

{{{ x = 1+root(3,2^16) }}}

The index of the root is 3,
the exponent of 2 is 16

So write the exponent in terms of its nearest multiple
of the index 3 which does not exceed 16.  So write the 16 
exponent as 15+1

{{{ x = 1+root(3,2^(15+1)) }}}

Then write {{{2^(15+1)}}} as {{{2^15*2^1}}} or just {{{2^15*2}}}

{{{ x = 1+root(3,2^15*2)) }}}

Then divide the exponent 15 by the index of the radical 3 and get 5

Then take the {{{2^15}}} out of the cube root as a {{{2^5}}} in front
of the radical:

{{{ x = 1+2^5*root(3,2) }}}

Then write the {{{2^5}}} as {{{32}}}

{{{x=1+32*root(3,2)}}}

Edwin</pre>