why does 0 to the power of 0 equal 1?
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I figured I’d add a second comment answering a closely related question, but is more well defined. Why are other numbers (besides 0) raised to the power 0 equal to 1. In other words why is x⁰=1 for x≠0. Every time you increment the power by 1, you multiply by the base. x^(n+1)=x•x^n and as an example 2⁵=32=2(16)=2•2⁴ which makes sense because for integer powers, were taught the exponentiation is repeated multiplication. 2⁴=2•2•2•2 and multiplying by one more 2 is just 2⁵.
Symmetrically, every time you decrement the exponent, you divide by the base. x^(n-1)=x^(n)/x and as an example 3³=27=81/3=3⁴/3. And if you keep dividing by 3, you’ll eventually get to 3¹=3. Divide by 3 once more and you get 3⁰=3/3=1 boom. And you can even keep going, 3^(-1)=1/3. And 3^(-2)=1/9=1/(3•3)
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