Multiplibonacci #3

From the solution to the previous problem , we know that the $n$ th Multiplibonacci number's power is always going to be the $n-1$ st Fibonacci number.

What about negative Multiplibonacci numbers? Well, we have to first define what a negative Fibonacci number is. We can do this by starting with 0 and 1, then working backwards. If we do this, we get the below sequence: $...-8,5,-3,2,-1,1,0,1$ As we can see, the negative Fibonacci numbers are equal to the positive Fibonacci numbers, except every other number is negative instead of positive. Because we want the -6th Fibonacci number (as -5-1=-6), we need to find the Fibonacci number 6 "steps" before 0.

Because 6 "steps" before 0 in the Fibonacci sequence lands us at -8, we have that ${ _{ -5 }{ M }_{ -5 } }={ (-5) }^{ (-8) }$ . ${ (-5) }^{ (-8) }$ rounded to the nearest thousandths place is $\boxed { 0.003 }$ , which is the correct answer.