Ok, so for obvious reasons 0^0 = 0 according to almost all the people reading the answer here, but here, 0^0 cannot be 0 Theoratically..... Let's take a number say, a^m, ie, a x a x a x a x a x a..... x a x a (m times) now, as we know any number to the power of 0 is 1, we will take any number, a^0 = 1 but..... since, a is a variable let's assume that a = 0..... now the point is according to the theory a^0 = 1 but when we assume a = 0 then a^0 cannot be 1 as, any number to the power of 0 is 0..... therefore according to our calculation and work done we stumble at, a^0 = 1 but when, a = 0 = a^0 = ? now the point is, what is 0^0..... 0^0 = ? For solving our problem let's take some real numbers (till 3 decimals) say, 1^1 = 1.000..... 0.9^0.9 = 0.909 0.8^0,8 = 0.836 0.7^0.7 = 0.779 0.6^0.6 = 0.736 0.5^0.5 = 0.707 0.4^0.4 = 0.693 We observe that the values are gradually decreasing but..... 0.3^0.3 = 0.696 0.2^0.2 = 0.724 0.1^0.1 = 0.793 Now we observe that the values are gradually increasing..... Let's go further..... 0.05^0.05 = 0.860 0.02^0.02 = 0.929 0.01^0.01 = 0.954 0.001^0.001 = 0.993 0.0001^0.0001 = 0.99907939..... 0.00001^0.00001 = 0.99988487..... 0.000001^0.000001 = 0.99998618..... Now we observe that the values are gradually increasing and it will surely reach 1...... Therefore 0^0 is actually = 1 but..... Since it is not practically not possible we leave it as undefined..... Hence, 0^0 = UNDEFINED.