How do you write #2^5/2^8# using only positive exponents?

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Answer 1 · 2018-03-30T12:13:38

#2^5/2^8=2^(5-8)=2^-3=1/2^3=1/8#

Answer 2 · 2018-03-30T12:16:34

#2^5/2^8 = 1/(2^(8-5)) = 1/2^3#

Subtract the indices as you normally would for division.

However, notice that the bigger index is in the Denominator.

#2^5/2^8 = (cancel2xxcancel2xxcancel2xxcancel2xxcancel2)/(cancel2xxcancel2xxcancel2xxcancel2xxcancel2xxcolor(blue)(2xx2xx2))#

#= 1/2^3#

Instead of expanding we could simply have subtracted #8-5#, but write the answer in the denominator

#2^5/2^8 = 1/(2^(8-5)) = 1/2^3#