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

1 Answer
Jan 24, 2017

Answer:

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#.