Exponential Form: Definition & Overview

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  • 0:04 Exponential Form Defined
  • 0:24 Converting to Exponential Form
  • 1:40 Logarithmic Form
  • 4:02 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
Algebraic expressions written in exponential form are expressions written with an exponent. This lesson will define exponential form, give some examples, and follow with a quiz to test your understanding.

Exponential Form Defined

The exponential form of an algebraic expression is an expression that includes an exponent. Any expression that includes an exponent is said to be written in exponential form. Here are a few examples to familiarize you:

x^2
3y^5
2^3

Converting to Exponential Form

In algebra, there are frequently different ways to express the same thing. The form that you choose to use depends on what will make the problem you are working on easier to solve or give you a solution in a way that is usable to others. Let's look at a simple example:

Convert 8 to exponential form.

8 = 2 * 2 * 2 = 2^3

This simple expression would be best used if you were trying to factor an expression and wanted to know how many 2s multiplied together were equal to 8.

Converting expressions to exponential form can also have uses when you are trying to add like terms or simplify expressions. For example:

Simplify the following:
2x^4 + x * x * x * x

Since we know when written in exponential form x * x * x * x = x^4, we can simplify that expression in the equation. The result of that simplification is 2x^4 + x^4. This can now be simplified again because the terms are like terms and can be added together. The result is 3x^4.

Logarithmic Form

A logarithm refers to the exponent in an algebraic expression written in exponential form. A logarithmic expression is the inverse of an exponential expression. Logarithms (logs) were introduced in the 17th century as a simpler way to solve algebraic expressions and were quickly adopted by scientists, engineers, and others to perform calculations more easily.

The rule for converting an expression written in logarithmic form to one written in exponential form is:

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In order to convert an expression in exponential form to one in logarithmic form, you just need to fill in a, b, and c to their proper places. Let's try it out.

Convert 3^2 = 9 to logarithmic form.

To do this, just plug the numbers in their respective places, like this:

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