Take
4^(5) = 4*4*4*4*4
4^(4) = 4*4*4*4
4^(3) = 4*4*4
4^(2) = 4*4
4^(1) = 4
4^(0) = 1
Going up in power means you multiply
4^(4) = 4^(3) * 4
Going down in power means you divide
4^(3) = 4^(4) / 4
So you can even extend this to negative numbers
4^(0) = 1
4^(-1) = 4^(0) /4 = 1/4
4^(-2) = 4^(-1) /4 = [ 1/4 ]/4 = 1/(4*4)
4^(-3) = 4^(-2) /4 = [ 1/(4*4) ]/4 = 1/(4*4*4)
4^(-4) = 4^(-3) /4 = [ 1/(4*4*4) ]/4 = 1/(4*4*4*4)
4^(-5) = 4^(-4) /4 = [ 1/(4*4*4*4) ]/4 = 1/(4*4*4*4*4)
Keep in mind dividing a fraction:
[ 1/2 ]/2
is the same as multiplying the denominator
[ 1/2 ]/2 = 1/(2*2) = 1/4
-“A half of a half is a fourth”-
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