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!
[…] #1 12. Common Pitfalls in A’levels Math #2 13. Common Pitfalls in A’levels Math #3 14. Why is anything to the power of 0 always 1? 15. Classical Mathematical Fallacies #1 16. Classical Mathematical Fallacies #2 17. Classical […]
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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