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

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.

${2}^{3} \cdot {4}^{4}$

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:

${2}^{3} \cdot {\left({2}^{2}\right)}^{4}$

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

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

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.