Question 1089464
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Let "x" be the number under the question.


Then the condition says


{{{(x*sqrt(x))^3}}} = 20000 - 317,   or, which is the same,   x^(9/2) = 19683,   or


{{{(sqrt(x))^9}}} = {{{3^9}}}.


It implies {{{sqrt(x)}}} = 3.


Hence,  x = {{{3^2}}} = 9.


<U>Answer</U>.  x = 9.


<U>Check</U>.  {{{x*sqrt(x)}}} = {{{9*3}}} = 27  and  {{{27^3}}} = 19683.  ! Correct !.
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Solved.