Question 134646
Nice problem!!!
Given : {{{((8^(x+1)/16^x))^(1/3) =32}}}
Cube both sides
{{{((8^(x+1)/16^x)) =32^3}}}
{{{(8^(x+1)) =32^3 * 16^x}}}
{{{ (8^(x+1))= (16*2)^3 * 16^x}}}
{{{ (8^(x+1))= 8 * 16^(x+3)}}}
{{{ 8^x = 16^(x+3)}}}
{{{ (16/2)^x = 16^(x+3)}}}
{{{ 2^(-x) = 16^3 }}}
{{{ 2^(-x) = (2^4)^3 }}}
x = -12

verify by plugging -12 back into the original equation
Thanks for the problem., it was fun