Expert: Sherry Wallin - 2/16/2011

Question
0/0=undefined........
0/0=(0*0)/0=(0/0)*0=0^0*0^1=0^(0+1)=0^1=0.....how??????

Answer
Will~

I can try to answer this step by step:
You are given that 0/0 is undefined and then there is a series of steps that is suppose to lead the conclusion. I will justify each step that I can:

0/0 = (0*0)/0 all that has been done hear is you have multiplied the top 0 by 0 which is still
= (0/0)*0  when there are 2 factors over the same denominator you can choose which factor goes over
          the denominator
= 0^0*0^1 this one really doesn't make much sense because the 0 power is not defined. If you use the
         rule that any nonzero number to the 0 power is 1 and remove the restriction on 0 you have
         0^0 = 1
= 0^(0+1) when the bases are the same we add the exponents
= 0^1  just simplification of 0+1
= 0 any number to the first power is the number itself

Check any beginning algebra book and you will see that any number to the zero power is 1 EXCEPT 0 and usually the text tells you just that the base cannot be 0 and doesn't define it if the base is 0.

Math Prof