why is x to the power of 0 always 1?

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I tried to google a proof, and i found that it comes from the formula: x^1*(1/x^1) where the two x^1s cancel eachother out. I wasn’t satisfied with the answer, so i am still somewhat confused.

Usually when there’s some math i don’t get, i try to imagine a scenario irl, where a formula would apply. This always helps, but i can’t find one here.

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9 Answers

Anonymous 0 Comments

Exponentiation is repeated multiplication. Raising the exponent by 1 is the same as multiplying the number by the base. In the same way, everytime the exponent is lowered by 1, you divide the total by the base.

2³ = 8 (2×2×2)

2² = 2³ ÷ 2 = 8 ÷ 2= 4

2¹ = 2² ÷ 2 = 4 ÷ 2= 2

Well,

2⁰ = 2¹ ÷ 2

= 2 ÷ 2

= 1

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