[{x ^ (3a-4)^ 2}/ {x^(2a-4)^3}]^ 3

Question

help he please!!

Answer 1

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)}