Question

How do you simplify `2^3*4^4`?

Answer 1

Substitute in `2^2` for 4, then simplify, and you'll end up with `2^11`, which equals 2048.

Explanation:

Let's first simplify the expression, then we'll solve it.

Let's first start with the original question:

`2^3*4^4`

Notice that we're working with 2 terms - one with a base of 2 and the other with a base of 4. But remember that `4=2^2`. So we can substitute and get:

`2^3*(2^2)^4`

When dealing with exponentials, when we take a power of a power (like with the `(2^2)^4` term, it's the same as multiplying the exponents, so we get that `(2^2)^4=2^(2*4)=2^8`. Let's plug that into our original question:

`2^3*2^8`

When we have a situation where two numbers with exponentials are multiplying that have the same base, we add the exponentials together, so here we'll get

`2^(3+8)=2^11`

So that's the simplified form. Solved, it equals 2048.