Question

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

Answer 1

`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*2*2*2*2` then we can expand both exponentials and see what we have.

So `2*2*2*2*2*2*2*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 * 2^3`
`2^(5+3)`
`2^8`

Hope this helps!