Here’s the explanation I like best:
2¹=2. Happy enough? Now multiply it by 2.
2¹×2=2²=4. And again.
2²×2=2³=4×2=8. And again.
2³×2=2⁴=8×2=16. And so on.
So multiplying by 2 is the same as increasing the power of 2 by 1. Now, dividing is just like undoing division. So dividing just *decreases* the power by 1, i.e.
2⁴÷2=2³=16÷2=8.
2³÷2=2²=8÷2=4.
2²÷2=2¹=4÷2=2.
So…
2¹÷2=2⁰=2÷2=1.
And we can push it further and say that negative powers give us fractions (except I can’t write negative powers on here)…
2⁰÷2=2^(-1)=1÷2=½
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