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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]

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