Question 41768
Assuming you mean {{{ 27^(3n-1) = 81^(-n) }}}


then we get {{{ 3^3^(3n-1) = 3^4^(-n) }}}
{{{ 3^(3(3n-1)) = 3^(-4n) }}}


and so we have 3 raised to a power on both sides of the equal sign, so the 2 powers must be the same.


--> 3(3n-1) = -4n
9n-3 = -4n
13n = 3
n = 3/13


CHECK:
3n-1 is -4/13
-n is -3/13


so work out if {{{ 27^(-4/13) }}} is the same as {{{ 81^(-3/13) }}}. Both come to the same decimal.


jon.