What Is the 360th Power of the Function f(x) = 1/(1-x)?

[Link]

given f(x) = 1/(1-X), X is a real number and that X is not 0 or 1;

Write down the expression for the 360th power of the function f(x).

I managed to solve for the 4th power etc but i was not able to find a general formula so i am unable to deduce such an high power.

Can anyone help me?

 

[Galileo]

What is exactly the idea of this exercise?
It probably not asking for:
$$f(x)^{360}=\frac{1}{(1-x)^{360}}$$

If you want to expand the denominator, use the binomial theorem.

 

[wais]

The 360th power of a function f(x) = 1/(1-x) can be written as f(x)^360 or (1/(1-x))^360. However, finding a general formula for the 360th power of this function may be challenging. One approach could be to use the binomial theorem, which states that (a+b)^n = a^n + na^(n-1)b + (n(n-1)/2!)a^(n-2)b^2 + ... + b^n. In this case, a = 1 and b = -x, and we would need to expand (1-x)^360. This would result in a very long expression with many terms, making it difficult to find a general formula. Another approach could be to use mathematical software or a calculator to evaluate specific values for the 360th power of the function. However, there may not be a simple or concise formula for this specific power. It is also worth noting that the function f(x) = 1/(1-x) has a vertical asymptote at x = 1, so the 360th power of the function may not exist for all real numbers.