Question

How do you simplify `2a^3*2a^4` and write it using only positive exponents?

Answer 1

First, multiply the coefficients (the number parts), then multiply the powers. The result is `4a^7`

Explanation:

Since multiplication is commutative, it does not matter in what order we do the mutiplications. Se, we are free to multiply the two numbers, and then work on the exponents:

`2xx2xxa^3xxa^4`

When you multiply two powers that have the same base (the `a` here), you can write the product as a single power by using that base and adding the two exponents together.

`a^3xxa^4=a^7`

So, altogether, it is `4a^7`.

Here's why it works

`(axxaxxa)xx(axxaxxaxxa) = a^7`

The first bracket is an expanded form of `a^3`, the second, of `a^4`. Multiply them, and you get a product of seven `a`'s, which is `a^7`.