ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Beginning Algebra Tutorial I--Exponents and PEMDAS

Updated on August 30, 2012

About Me

Hello and Welcome!!! My name is Patty. I am 37 years old, married, mother of four wonderful children, and recently awarded my Associates Degree in Computer Science.

While working towards my degree, Algebra was one of the hardest subjects for many students. In this tutorial, I will cover a brief introduction to some of the very basic rules of Exponents and the Order of Operations (PEMDAS).

I hope this tutorial serves as a review or helps those just learning this material for the first time. In the near future, I do plan on adding more advanced tutorials.

Lesson One---Exponents

*Note that this symbol is often used as the multiplication symbol.

Exponents can seem intimidating to some. Exponents are used for repeated multiplication. For Example instead of saying 2 • 2 • 2 • 2 • 2 • 2, the shorter way would be to use exponents in this case 26 or "two to the sixth power".

In the example above the 2 is the base number and the 6 is the exponent.

Another way exponents are shown is using this symbol ^ to show the base raised to a certain power.

Examples:

  • 102 would look like 10 ^ 2.
  • x5 would look like x ^ 5

Below is just some of the very basic rules which will be covered below.

In the chart below, the variable x is the base and n and m are exponents.

Very Basic Exponent Rules

Exponent Rules Example One

xn Whatever x is equal to, multiply that same number n amount of times.

Exponent Rules Example Two

x0 = 1 Any base raised to the 0 power is ALWAYS equal to 1.

Exponent Rules Example Three

xm • xn = xm + n As long as the variable is the same just add the exponents.

Exponent Rules Example Four

xm / xn = xm - n As long as the variable is the same just subtract the exponents.

Lesson Two--PEMDAS

Lets begin with the Order of Operations. When solving an equation or simplifying an expression, solve/simplify in this order:

  1. Parenthesis (first solve what is in the parenthesis and/or brackets)
  2. Exponents (then evaluate the exponents ex. 23 = 2 x 2 x 2 = 8)
  3. Multiply and/or Divide (from left to right)
  4. Add and/or Subtract (from left to right)

One way I was taught to remember this rule:

"Please Excuse My Dear Aunt Sally!"


PEMDAS Examples

In the examples below, I will attempt to show you how to solve the problems step-by-step.

Problem 1: 5 ^ 2 • (10-8)

52 • (10-8) = ?

  • First solve what is in the Parenthesis (10-8) = 2
  • Now we have 52 • 2 = ?
  • Then Evaluate the Exponent 52 = 5 • 5 = 25
  • Now we have 25 • 2 = ?
  • Finally Multiply and solve: 25 • 2 = 50

Problem 2: (7 • 2) - [ 9 ÷ (8 ÷ 8) ]

(7 • 2) - [ 9 ÷ (8 ÷ 8) ] = ?

At first glance this problem may seem tricky. In this example, we work with the innermost parenthesis, the parenthesis inside the brackets.

  • First solve what is in the innermost Parenthesis (8 ÷ 8) = 1
  • Now we have (7 • 2) - [ 9 ÷ 1] = ?
  • Then solve what is in the Brackets [ 9 ÷ 1] = 9
  • Now we have (7 • 2) - 9 = ?
  • Then solve what is in the Parenthesis (7 • 2) = 14
  • Now we have 14 - 9 = ?
  • Finally Subtract and solve: 14 - 9 = 5

Problem 3: (8 - 2 * 4 + 3 ^ 2) / 6 ( 2 - 1)

(8 - 2 • 4 + 32 )
-------------- = ? 
6(2 - 1) 

This problem may seem a little overwhelming at first. With this type of problem, the fraction bar acts as a type of Parenthesis. We will start with simplifying the top and then the bottom.

  1. On the top we will start with the Exponent 32 = 3 • 3 = 9
  2. On the top we now have 8 - 2 • 4 + 9 = ?
  3. Now the Exponent is gone we move to Multiplication 2 • 4 = 8
  4. On the top we now have 8 - 8 + 9 = ?
  5. Reading from left to right we are left with Subtraction and Addition 8 - 8 = 0
  6. Now on the top we have 0 + 9 = 9
  7. On the top we are left with 9
  8. On the bottom we have 6 ( 2 - 1) = ?
  9. First solve what is in the Parenthesis (2 - 1) = 1
  10. On the bottom we now have 6 ( 1 ) = 61 = 6 *Note the Parenthesis act as a multiplication symbol.
  11. On the bottom we are left with 6
  12. Now we combine the top and the bottom 9 / 6
  13. Simplify the fraction and the final answer is 3 / 2

Test Yourself

view quiz statistics

Final Thoughts

I hope that this tutorial gave you a very basic understanding of the basic rules of Exponents as well as the Order of Operations, PEMDAS.

Take the test on the right to test what you have learned!! If you scored low at first...try, try again. Re-read this article, follow along with the samples provided and try the test again.

For those just learning, remember Math can be hard when first learned, but with practice and determination...Anything is possible!!!

Thank-you for taking the time to read this article. GOOD LUCK and NEVER GIVE UP!!!

If you like this tutorial, you may want to check out my next tutorial on Beginning Algebra Tutorial II--Evaluating Expressions and Solving Equations.


Comments

    0 of 8192 characters used
    Post Comment

    • Patty Kenyon profile imageAUTHOR

      Patty Kenyon 

      6 years ago from Ledyard, Connecticut

      Anon, I am actually in the process of redoing this Hub with more visual aids...Nice catch, I will definitely fix that when I redo the Hub!!! THANKS AGAIN!!!

    • profile image

      Anon 

      6 years ago

      Nice tutorial.

      Problem 3: 8 - 2 * 4 + 3 ^ 2 / 6 ( 2 - 1)

      You should enclose 8 - 2 * 4 + 3 ^ 2 inside parentheses to indicate that all of them are included in the numerator. Otherwise, only 3 ^ 2 would be considered to be on top of the fraction bar.

    • Patty Kenyon profile imageAUTHOR

      Patty Kenyon 

      6 years ago from Ledyard, Connecticut

      IntegrityYes, Thank-you sooo much!!! I plan on re-doing this hub and adding more as well as doing other tutorials!!! As Always, I appreciate your support!!!! :)

    • profile image

      IntegrityYes 

      6 years ago

      OOH!,Patty! HAH-HAH! That is nice and informative. Many need to see it. I voted up,my friend.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: https://hubpages.com/privacy-policy#gdpr

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)