SOLUTION: Why does the base to the power of zero equal one?

Algebra.Com
Question 200002: Why does the base to the power of zero equal one?
Answer by RAY100(1637)   (Show Source): You can put this solution on YOUR website!
Just a brief review
.
a = a^1,,,,,, a*a = a^2,,, a*a*a = a^3,,,,etc
.
if we had a^3 /a^2 = (a*a*a) / (a*a) = a,,,,,or a^(3-2) = a^1 =a
.
Now if we had a^3 /a^3 = (a*a*a) / (a*a*a) =1,,,,,,or a(3-3) = a^0
.
Therefore we have a^0 = 1
.

RELATED QUESTIONS

Why does anything to the power of zero equal... (answered by pwac)
why does any base to the zero power =... (answered by jim_thompson5910)
Why is any number that is raised to the power of "zero" equal... (answered by JC)
why is something raise to the power zero equal to one. for example 3^0=1... (answered by longjonsilver)
One of my assessment questions was: "What is 2.3 x 10 in exponential notation?" My (answered by jim_thompson5910)
why is 3 to the zero power equals... (answered by Mathtut,MathTherapy)
Why does a base number to the exponent of zero equals 1? When a number is multiplied... (answered by math_tutor2020,MathTherapy)
why does 4 to the 8 power divided by 4 to the 2 power equal to... (answered by Alan3354)