How do you simplify the expression 2^5/(2^3 times 2^8)?

Jun 21, 2016

${2}^{5} / \left({2}^{3} \times {2}^{8}\right) = \frac{1}{2} ^ 6$

Explanation:

${2}^{5} / \left({2}^{3} \times {2}^{8}\right)$

= ${2}^{5} / \left({2}^{3} \times {2}^{3 + 5}\right)$

= ${2}^{5} / \left({2}^{3} \times {2}^{3} \times {2}^{5}\right)$

= $\frac{1 {\cancel{2}}^{5}}{{2}^{3} \times {2}^{3} \times {\cancel{2}}^{5}}$

= $\frac{1}{{2}^{3} \times {2}^{3}} = \frac{1}{2} ^ \left(3 + 3\right) = \frac{1}{2} ^ 6$