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

Jan 24, 2017

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

#### 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:

$2 \times 2 \times {a}^{3} \times {a}^{4}$

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.

${a}^{3} \times {a}^{4} = {a}^{7}$

So, altogether, it is $4 {a}^{7}$.

Here's why it works

$\left(a \times a \times a\right) \times \left(a \times a \times a \times a\right) = {a}^{7}$

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 ${a}^{7}$.