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

Mar 30, 2018

${2}^{5} / {2}^{8} = {2}^{5 - 8} = {2}^{-} 3 = \frac{1}{2} ^ 3 = \frac{1}{8}$

Mar 30, 2018

${2}^{5} / {2}^{8} = \frac{1}{{2}^{8 - 5}} = \frac{1}{2} ^ 3$

#### Explanation:

Subtract the indices as you normally would for division.

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

${2}^{5} / {2}^{8} = \frac{\cancel{2} \times \cancel{2} \times \cancel{2} \times \cancel{2} \times \cancel{2}}{\cancel{2} \times \cancel{2} \times \cancel{2} \times \cancel{2} \times \cancel{2} \times \textcolor{b l u e}{2 \times 2 \times 2}}$

$= \frac{1}{2} ^ 3$

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

${2}^{5} / {2}^{8} = \frac{1}{{2}^{8 - 5}} = \frac{1}{2} ^ 3$