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Exponents, Exponential Notation, and Scientific Notation

A series of free Basic Algebra Lessons from Brightstorm online Algebra series.

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.

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.

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.

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.

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