Question 179694
 (5y-4)^-1/4 - 5(5y-4)^-4/3 =0
 (5y-4)^(-3/12) - 5(5y-4)^(-16/12) = 0

----
[(5y-4)^(-16/12)][(5y-4)^(-12/12) - 5] = 0

[(5y-4)^(-16/12)][(5y-4)^-1 - 5] = 0

Solve for "y":

(5y-4)^(-16/12) = 0 or (5y-4)^(-1) = 5

y cannot equal 4/5 because the exponent is negative:
-----------
Solve (5y-4)^-1 = 5
Invert to get:
5y-4 = 1/5
5y = (1/5)+4
5y = 21/5
y = 21/25
=================
Cheers,
Stan H.