this post was submitted on 11 Oct 2023
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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.