AtoZ Math Academy

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1. To prove that anything raised to a power of zero is one
2. To prove that 0! = 1

1.
a^x * a^y = a^(x+y)

Let x= 0.

a^0 * a^y = a^o+y

a^0 * a^y = a^y

a^o = a^y /a^y.

a^0 = 1.

2.
Recall that n! = n(n-1)(n-2) * ....*3*2*1
n! = n(n-1)!
If we put n=1.
Then, 1! = 1(1-1)! = 1.0!
So in our factorial notation, de define 0! =1.