Question 615239
{{{ (1/9)^3x=27 }}}
Note That {{{ 1/9 = (1/3)^2 }}}, so
{{{ (1/9)^(3x) = 27 }}}
{{{ ((1/3)^2)^(3x) = 3^3 }}}
{{{ ( 1/3 )^(6x) = 3^3 }}}
I can take the cube root of both sides
{{{ (1/3)^(2x) = 3 }}}
{{{ ( 1/3 )^(2x) = (1/3)^(-1) }}}
{{{ 2x = -1 }}}
{{{ x = -1/2 }}}
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check:
{{{ (1/9)^3x=27 }}}
{{{ (1/9)^(3*(-1/2))=27 }}}
{{{ (1/9)^(-3/2) = 3^3 }}}
{{{ ((1/3)^2)^(-3/2) = 3^3 }}}
{{{ (1/3)^(-3 ) = 3^3 }}}
{{{ 1 / (1/3)^3 = 3^3 }}}
{{{ 3^3 = 3^3 }}}