Lesson Objective

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

About This Lesson

This lesson is a continuation from the lesson Exponent Laws - Part 1.

The next three laws that you are going to learn can be derived from the first three laws shown in Part 1. So, the ideas behind these laws are not completely new.

Again, it is important for you to understand these laws before using them. This helps to minimize mistakes.

Tip #1

Let's recall the first three exponent laws before proceeding further. The picture below shows the 1^st law. Here is an example on how to use it:

       6a¹⁰ x 3a^-5 = 6 x 3 x a¹⁰ x a^-5
                       = 18 x a^{10 + (-5)}
                       = 18 x a^{10 -5}
                       = 18a⁵

Tip #2

As for the 2^nd law of exponent, the picture below shows the law. Here is an example on how to use it:

       6a¹⁰ ÷ 3a^-5 = 2a¹⁰ ÷ a^-5
                       = 2a^{10 - (-5)}
                       = 2a^{10 + 5}
                       = 2a¹⁵

Tip #3

Finally, for the 3^rd law of exponent, the picture below shows the law. Here is an example on how to use it:

           2(a¹⁰)^-5 = 2 x a^{10 x (-5)}
                       = 2a^-50
                     

Tip #4

You may come across terms like a¹ or 2¹. These terms simply mean that:

                              a¹ = a     
                              2¹ = 2

We can explain them using the following observation:

                             2³ = 2 x 2 x 2
                             2² = 2 x 2
            Therefore:   2¹ = 2

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