Question 1199223
.
<pre>

{{{root(5,(5sqrt(700)-sqrt(7))^6)}}}

= {{{root(5,(5*10sqrt(7)-sqrt(7))^6)}}}

= {{{root(5,(50sqrt(7)-sqrt(7))^6)}}}

= {{{root(5,(49sqrt(7))^6)}}}

= {{{root(5,(7^2)^6*7^3)}}} = {{{root(5,7^(12+3))}}} = {{{root(5,7^15)}}} = {{{7^3}}} = 7*7*7 = 343.
</pre>

Solved.