So, I have the following code in R:
y a <- -0.1 test <- (1/((y+as.numeric(!y))*(a-1))) test test^a -0.9090909^a
Giving me the
-0.9090909 ^ a is the same as -(0.9090909 ^ a). Notice the parentheses.
-0.9090909 ^ a
-(0.9090909 ^ a)
However, your test contains negative values, and you cannot take the root of a negative number. Try (-0.9090909) ^ a to verify this:
test
(-0.9090909) ^ a
> (-0.9090909) ^ -0.1 [1] NaN