# Polynomial Functions: Exponentials and Simplifying

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Exponentials, Logarithms & the Natural Log

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:34 ''x'' to the ''n''th Power
• 1:43 Powers in Daily Life
• 2:30 Polynomials
• 3:26 Properties of Polynomials
• 7:07 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay
Speed

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Robert Egan
How do we keep track of a rapidly multiplying population of bunnies? Well, those are simply powers of 2. Review powers and simplify problems with exponents in this lesson.

## Bunnies Galore

Have you ever heard of that bunny problem? You know, the one where you start out with one bunny, and then all of a sudden you have two bunnies, and each of those bunnies has a bunny, so you end up with four bunnies? Each of those bunnies has a bunny, and you have eight bunnies and then 16 and 32 and 64 - your population just keeps growing!

## x to the nth Power

You could've said that your population started out with one times two bunnies times two bunnies times two bunnies and so on and so forth. If we ignore that one, because it doesn't really matter in this case, you end up with a case of repeated multiplication: 2 * 2 * 2 * 2 * 2 ... When x=2, we can write this as x * x * x * x * x ... and so on and so forth, which gives us x^n. Now, in x^n, x is the base, n is the exponent, and we call this x to the nth power. In the case of our population, we had 2 * 2 * 2 * 2 * 2, and let's just cap it off there. So we have five 2's for a population of 2^5.

## Powers in Daily Life

Now these powers are used all over in math and really all over the world. For example, if we want to look at mummies and know how old they are, we use an approach like carbon dating. And, carbon dating is used with powers, which might be something like 2.7^-t, where t is time. So we're using a power to determine the age of a mummy. Another example is the metric system. In the metric system, we're using powers that look like 10^x meters. Now, if x=-10, you're looking at something about the size of an atom. If x=20, you're looking at something roughly the size of the galaxy.

## Polynomials

One type of power that we look at and care about a lot is polynomials. So we care about x to the nth power, where n is some number, and we care about these because they are things like x or x^2, which is x * x, or x^3, which is x * x * x. In general, we care about x^n. Now let's look at some properties of x^n. We know that x^1=x, but what about x^0? Well, x^0 is NOT equal to zero. Instead, x^0=1. It's a little strange, but if you think about it, you have to start somewhere.

## Properties of Polynomials

So what are the properties?

To unlock this lesson you must be a Study.com Member.

### Register to view this lesson

Are you a student or a teacher?

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.