# How do you simplify 2^5/2^3 times 2^8?

Jun 2, 2016

Use the following exponent rules:

•Quotient rule: ${a}^{n} / {a}^{m} = {a}^{n - m}$
•Product rule: ${a}^{n} \times {a}^{m} = {a}^{n + m}$

#### Explanation:

Let's calculate the ${2}^{5} / {2}^{3}$ first.

Applying the quotient rule we get:

${2}^{5} / {2}^{3} = {2}^{5 - 3} = {2}^{2}$

Now, we must calculate ${2}^{2} \times {2}^{8}$

By the product rule:

${2}^{2} \times {2}^{8} = {2}^{2 + 8} = {2}^{10}$

Now, knowing our final result, we calculate ${2}^{10}$ which gives 1024.

Hopefully this helps!