When power of any number have 0 then it gives a value equal to 1. Why ?

Power means the number of times the digit is supposed to be multiplied by itself. ex- you can write 2 = 2 x 1 = (2^1) x 1. here you are multiplying "2" only one time to itself. Similarly u can have: 2 = 2 x 1 = (2^1) x 1 4 = 2 x 2 x 1 = (2^2) x 1 8 = 2 x 2 x 2 x 1 = (2^3) x 1 So all the numbers are implicitly a multiple of 1(the multiplicative identity, which when multiplied with any number, gives nothing but the original number). Similarly for 2^0 = 1 (because you are multyplying 2 to itself "0 mumer of times". So what you are left with is 1, the multiplicative identity.) ********************************************* Another way to see it may be this : If you have a number raised to some power,say x^a, and the same number raised to another power,say x^b, you can add the exponents while multiplying them. So, x^a X x^b = x^(a+b). Now, raising a number by a positive power is multiplying by itself that many number of times, but raising a number with a negative power means dividing the number with itself that many times. So, x^1 = x. and x^(-1) = 1/x. If a and b are equal and opposite in sign then, a = -b. So, x^a + x^b = x^(a+b), x^(-b) + x^b =x^(-b+b) If we put numbers in the place, taking x = 3, a = 2, b = -2, then x^(-b) + x^b = x^(-b+b) 3^(-2) + 3^2 = 3^(-2+2) 1/(3x3) +(3x3) = 3^0 1/9 x 9 = 3^0 You see, where we are approaching? 3^0 =1. This is true for all numbers except the base of "0" where 0/0 is an indeterminate form. because, you can always divide something(anything greater than 0) into 1 parts to infinity parts, but you cant tell what happens when you divide "nothing(0) into no(0) parts" There are a few other explanations here :http://scienceline.ucsb.edu/getkey.php?key=2626 read less