# Why is anything the power of 0 always 1?

Now I know this is one known fact that students just accept. Why is it that anything raised to the power of 0 is 1? We know that , meaning we take the 2 and multiply it three times. So wouldn’t mean we multiply 2 zeroth times, and get back 2? So thats baffling.

This can be solved intuitively, like how we looked at previously. We can look at as the number of ways to arrange a set of number with numbers from to numbers.

Consider . This means we arrange the set of 3 numbers where the numbers are just 1 and 2. So we have

And we find the number of ways to be eight!

• Aravindan Sai Narayanan

0^0 is undefined.It doesn’t make sense to say that 0^0 is always one.To overcome this problem when a function of the form f(x)^g(x) has f(x) approaching zero as x tends to a and thus,f(x) approaches zero and when x tends to a given point a ,g(x) approaches zero.Thus,as x tends to a ,we have f(x)^g(x) as 0^0.0^0 can be any value and to overcome this indeterminate form, we need to first transform it to 0*infinity form; followed by changing it to infinity/infinity or 0/0 form;afterwhich,we apply L Hospital’s Rule to evaluate the limit as x tends to a.Other indeterminate forms include infinity^0, 0^infinity,1^infinity ,0*infinity,infinity-infinity, infinity/infinity and 0/0.See the attached link for more and detailed information about indeterminate forms /Users/akshayleninsingapore/Downloads/Indeterminate_form.pdf