Exponents

Before you start to explore how to multiply polynomials, it is important that you know how to handle exponents. You need to know how to multiply and divide terms that contain exponents. This is a quick overview of the rules of exponents. For a more comprehensive look at exponents, you can refer back to Algebra A.

Rule 1

When multiplying two powers, add exponents of the same base

You can see why this rule works by examining the example below:

Example

Multiply the following: (2²)(2³).

Solution

According to the rule above, since we have the same base in both powers we add the exponents. But WHY do we do this? To examine the reason behind the rule, let's expand each of the powers below.

Therefore...

(2²)(2³) = 2 x 2 x 2 x 2 x 2

OR...

Notice that the exponents of the original two powers (2 and 3) were added to get an exponent of 5 in our resultant power.

Take a look at the following examples:

Rule 2

When dividing powers, subtract exponents of the same base (top exponent - bottom exponent)

Again, let's explore an example that will illustrate why this rule works:

Example

Perform the following operation:

Solution

Again, expand each of the powers found in the numerator and the denominator:

We can divide out (cancel) five of the x's in the numerator with all of the x's in the denominator. In essence, we will eliminate the highlighted x's shown below:

This leaves us with the statement x·x·x or x³.

Notice again that we took the exponents of the original powers (8 and 5) and subtracted them to get an exponent of 3.

Rule 3

The last rule to keep in mind is:

Any power raised to an exponent of 0 is equal to 1

This means that .

There is no sample question sheet for this lesson online as you will get practice multiplying powers in the lesson on multiplying polynomials. You can also refer back to the pages on exponents in Algebra A.