ANSWER
[tex]x = - 3[/tex]
EXPLANATION
The given equation is
[tex]27^{1-x} =\frac{1}{9^{2x} }[/tex]
Recall that
[tex] \frac{1}{ {a}^{m} } = {a}^{ - m}[/tex]
Apply this rule on the right hand side to get,
[tex]27^{1-x} =9^{ - 2x} [/tex]
Express both sides to base 3.
[tex]3^{3(1-x)} =3^{2( - 2x)} [/tex]
Equate the exponents:
3(1-x)=2(-2x)
Expand:
[tex]3 - 3x = - 4x[/tex]
Group like terms,
[tex]4x - 3x = - 3[/tex]
[tex]x = - 3[/tex]
