this post was submitted on 11 Oct 2023
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I know I'm bad at math but I don't understand how 2x0=0 but 2^0=1
How are they different answers when they're both essentially multiplying 2 by zero?
Someone with a bigger brain please explain this
Edit: I greatly appreciate all the explanations but all they've done is solidify the fact that I'll never be good at math ๐ญ
2^0 isn't multiplying by zero. Considering this law: 2^a / 2^b = 2^(a-b)
it's obvious why 2^0 = 1
If a=b you're dividing by the same number resulting in 1.
Unfortunately, I cannot explain/prove the first law though.
The first rule is just simple division:
(2x2x2x2) / (2x2) =
(2/2) * (2/2) * 2 * 2=
1 * 1 * 2 * 2 =
2 * 2 =
4
Writing in terms of powers:
(2^4) / (2^2) =
(2^(4-2)) =
(2^2) =
4
The two bottom 2's "cancel out" (really they just divide into one another to make 1's) two of the top 2's and you're left with two top twos.