Question 699203
{{{ (x-2)^3/4 = 8 }}}
{{{ (x-2)^3/4 = 2^3 }}}
{{{ ( (x-2)^(1/4) )^3 = 2^3 }}} 
Take the cube root of both sides
{{{ ( x- 2)^(1/4) = 2 }}}
Raise both sides to the 4th power
{{{ x - 2 = 16 }}}
{{{ x = 18 }}}
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check:
{{{ (18-2)^3/4 = 8 }}}
{{{ 16^(3/4) = 8 }}}
{{{ ( 16^(1/4) )^3 = 8 }}}
{{{ 2^3 = 8 }}}
{{{ 8 = 8 }}}
OK