Answer:
x^-6
Step-by-step explanation:
You want to simplify the expression 27^(-2log3(x)).
Rules of logarithms
The applicable rules of logarithms are ...
log(a^b) = b·log(a)
b^(logb(a)) = a
Application
The rewrite can proceed like this:
[tex]27^{-2\log_3(x)}=(3^3)^{-2\log_3(x)}}=3^{-6\log_3(x)}=3^{\log_3(x^{-6})}=\boxed{x^{-6}}[/tex]
