Exponents, Exponential Notation, and Scientific Notation

A series of free Basic Algebra Lessons.

In this lesson, we will learn

  • an introduction to exponents and rules of exponents
  • multiplication and division properties of exponents
  • zero and negative exponents
  • scientific notation
  • simplifying expressions with exponents



Introduction to Exponents - Rules of Exponents

Since we often see exponents throughout all math courses, it is important to understand the rules of exponents. We need to understand how to distribute, add, multiply and divide exponents in order to simplify expressions or manipulate equations that have exponents. The rules of exponents, like those involving multiplication of terms, are important to learn and will be used throughout Algebra I and II and Calculus.

How to understand the vocabulary of exponents.



Multiplication and Division Properties of Exponents

There are different rules to follow when multiplying exponents and when dividing exponents. If we are multiplying similar bases, we simply add the exponents. If we are dividing, we simply subtract the exponents. If an exponent is outside the parentheses, it is distributed to the inside terms. It's important to understand the rules of multiplying exponents so that we can simplify expressions with exponents.

The following video is on Multiplying Exponents and the Exponent Rule

The following video is on Dividing Powers in terms of the Exponent Rule. 

The following video is on the Exponent Rule of a Power of a Power.



Zero and Negative Exponents

It's important to understand what It means to have negative exponents and zero exponents. Negative exponents put the exponentiated term in the denominator of a fraction and zero exponents just make the term equal to one. We can use negative exponents for cancelling with positive exponents while solving equations or simplifying expressions, although we need to keep in mind the rules of multiplying exponents.

This video explains zero exponents

This video explains negative exponents.



Scientific Notation

In the applied sciences, scientific notation is often employed as a method of notation for ease of writing and reading. When dealing with real world situations, the numbers we get as solutions are rarely whole numbers and scientific notation gives us rules to follow when using ugly numbers that have a lot of decimal places. In order to understand scientific notation, we must also have a solid understanding of exponents.



Simplifying Expressions with Exponents

We can use what we know about exponents rules in order to simplify expressions with exponents. When simplifying expressions with exponents we use the rules for multiplying and dividing exponents, and negative and zero exponents. In Algebra and higher math courses such as Calculus, we will often encounter simplifying expressions with exponents.

This video provides examples of simplifying exponential expressions using a several exponent rules (positive exponents). 



This video provides several examples of how to simplify exponential expressions containing negative exponents.




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