Question

Why does the n+1 and (1-n) cancel out?
$4 {}^{n + 1} \times 4 {}^{1 - n} \times 4 {}^{2} \\ = 4 {}^{n + 1 + (1 - n) + 2} \\ = 4 {}^{4} \\ = 256$
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Answer 1

The rule being used is $a^b*a^c = a^{b+c}$

You add the exponents when multiplying exponentials like this with the same base.

The n+1 adds with 1-n so that the n terms cancel out

n+(-n) = n-n = 0n = 0

The '1's dont cancel out though.