To simplify [{x^(3a-4)^ 2}/ {x^(2a-4)^3}]^ 3
ignoring the power of 3 for the moment, we have
{x^(3a-4)^ 2}/ {x^(2a-4)^3}
expanding the powers,
{x ^(9a^2 - 24a + 16)}/ {x^(8a^3 - 48a^2 + 96a - 64)}
The powers of x on the bottom (denominator) are negative, so subtract those powers from the powers of x on the top.
x^{(9a^2 - 24a + 16) - (8a^3 - 48a^2 + 96a - 64)}
x^(-8a^3 + 57a^2 - 120a + 80)
x^{-(a-4)*(8a^2-25a+20)}
now add on the cube power that we ignored at the beginning,
x^{-3(a-4)*(8a^2-25a+20)}