# How do you evaluate the expression 2^5*2^3 using the properties?

May 25, 2017

${2}^{8} = 256$

#### Explanation:

When we multiply exponentials, we can add the exponents together if the base is the same. We can prove this by expanding the exponents.

Since ${2}^{5}$ is $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ then we can expand both exponentials and see what we have.

So $2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ is what we get after expanding both ${2}^{5}$ and ${2}^{3}$. This is equal to ${2}^{8}$ since it is eight twos multiplied by each other.

Using the property it looks more like this:

${2}^{5} \cdot {2}^{3}$
${2}^{5 + 3}$
${2}^{8}$

Hope this helps!