Lesson Objective

This lesson shows you the basics behind the first three exponent laws. You'll learn how these laws are actually formulated...

About This Lesson

Let's say you need to find out the result (in the form of 2^???) of the multiplication of the numbers below:

                2¹⁰⁰⁰ x 2¹⁰⁰⁷

Now, if you try to solve it by calculating the actual value of 2¹⁰⁰⁰ or 2¹⁰⁰⁷, you will soon realize that it is very difficult to do so.

Fortunately, with the help of the first exponent law, you will quickly know that:

       2¹⁰⁰⁰ x 2¹⁰⁰⁷ = 2^{1000 + 1007}
                          = 2²⁰⁰⁷
 
This lesson shows you the basics behind the first three exponent laws. It is good to understand these laws first before using them.
             

Tip #1

When you are given a term with a form of a^m,
it is defined that:

                    a  is the base
                    m is the exponent

For example, consider the term 2⁵, referring to the definition above:

                    2 is the base
                    5 is the exponent

Tip #2

It is very important to understand how the exponents laws are formulated. Once you fully understood them, it's easier to avoid mistakes when applying these laws.

For example, usually those who don't understand the logic behind these laws will tend to make this mistake:

                     2³ x 2² = 2^{3 x 2} (wrong application of the first law)
                               = 2⁶
                               = 64     (oops!!...mistake)

When you use your calculator to check, you will find out that actually:
                    
                     2³ x 2² = 8 x 4
                               = 32     (correct!)

So, do realize the consequences for applying the exponent laws without  understanding them.

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