THE BASICS OF EXPONENTS

Exponents are sometimes called power. Mostly, it's a small-text number (or letter) found in the upper right corner of the base. All numbers and variables have an exponent, and that is "1". The "1" exponent tells that there's only one base. The base is a number or a letter (representing variable) as an expression. See the illustration below.

The red ones are the base(s) and the blue ones exponent(s)

Take note that the base(s) can any variable or integer. Don't get confused if you see base(s) different than ours. The illustration above is the introduction of the exponential concept.

On this page, we will be learning how to factor the exponential expressions.

The illustration below shows the 'basic' of exponent properties. Where the "a" is the base, and "m" as power, is the exponent. The exponent "m" is the one who tells how many base(s) are there in the exponential expression.

Common confusions about the power "m" are, students, tend to multiply "m" to the base "a", and it goes like "a x m =am". In this presentation, the author reminds every learner that we should be careful how to deal with this expression. Below are a few Illustrations of how this works.

Let "x" be our base this time, and "n" is the exponent. So,

is our exponential expression.

Illustration:

Given the exponential expression below,

The illustration tells us that the base 'x' was doubled by itself because of the power that says the base is twice by itself. The expression is factored out to x.x. Hence the power of each x is "1".

Let's take a look at the second illustration with a twist. In this example, there's a parenthesis on our base which is 2x, with a power of 2. The power simply tells that we have two 2x's.

Once again, it looks like we had two bases. But since it was enclosed in parenthesis, it means one. In this example, '2x' is the base. Don't get confused. The parenthesis is our basis. Hence 2 and x are inside the parenthesis, which means we have 2 and x as our base. So we ended at

as the final result if we're going to apply its power.

Here's another setting, where an integer (2) and variable (x) as the base has no parenthesis. Be reminded that 2 has power which '1', and x '2'. See number 3 below.

Notice that only 'x' was made double. So only 'x' was expanded or factored out. The '2' was not factored out hence the power tells that the base '2' is just itself.

Let's continue and see if you now find yourself comfortable with its basics.

Do you think we factored out number 4 right? (See below)

What is the factored out form of numbers 5, 6, and 7? (See below)

Now, for additional skills and recognition, I want you to answer the following tests as practice. Click the blue link below.

Click here to start your test!

Scores and its indications;

5 points > Extraordinary

4 points > Awesome

3 points > You're doing great

2 points > You just missed something

1 point > Redo the trial

Now you have the basic idea of how this works. Below were the provided expressions with solutions so you can check if your progress is doing ok. You can ask questions from the comment section at the bottom of this page.

Sample problems with Solutions.

Factor the given exponential expressions.

Since you are already familiar with the operations, try to take a simple test provided below. You can put your answer on a lined paper or in the blank. Just click on it and it will redirect you to another page. You don't have to do it quick. Just take your time.

Sample with partial Solution:

Let's have examples but the solution was given partially. Factor the given exponential expressions. Note, to avoid confusion with (.) as multiplication we used before, we use the (*) this time to mean multiply. Write your answer in replacement for the question mark(s). Let us give you an example;