Question 131755
You probably mean:{{{root(3,512x^8/y^3)}}}


First, you have to know and recognize the first few perfect cubes:
2^3=8
3^3=27
4^3=64
5^3=125
6^3=216
7^3=343
8^3=512


Secondly, you must know that perfect powers with exponents must be multiples of 3:  x^3, x^6, x^9, etc,


Now, {{{root(3,512x^8/y^3)}}}
{{{root(3,512x^6/y^3)*root(3,x^2)}}}
{{{(8x^2/y)*root(3,x^2)}}}


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