ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Index Notation And The Zero Power Rule

Updated on August 17, 2019
mathsoneminute profile image

We are a group of mathematics lovers that always looking to find the mystery of Mathematics! Feel free to join us and be a part of us!

Index Notation and The Zero Power Rule

Index notation is an important element in the development of mathematics. The use of positive indices was introduced by Rene Descartes back to the year 1637, a well-known French mathematician. Another well-known British mathematician, Sir Isaac Newton developed the field of index notation and introduced negative indices and fractional indices.

In the modern day, the development of technology not only makes most of our daily tasks easier, but it also saves the cost of expenses in various fields. One of the example, the use of memory cards in the digital camera enables users to store photographs in large number. In the early stage, memory cards were made with a capacity of 4MB. The capacity of memory cards was then increased to Gigabytes (GB).

Something you do not know is the capacity of memory cards is calculated using Index notation form, 2n. Index notation is normally written as = an, where a is base and n is index.

One of the popular rules in Index notation is The Zero Power Rule. What is the zero power rule and What is the value of a0? b0? 10? 20?

It might be easy if we could just press the calculator and get the value of 10= 1 and 20 = 1. The problem is how to prove it?

To prove it, let see the example below :

We all know that

21 = 1 x 2 = 2

22 = 2 x 2 = 4

23 = 2 x 2 x 2 = 8

24 = 2 x 2 x 2 x 2 = 16

25 = 2 x 2 x 2 x 2 x 2 = 32 , how about 20 ?

The answer is 20 = 1, but why?

The simplest way to explain it using the example above is like below :

25 = 2 x 2 x 2 x 2 x 2 = 32 (Divide by 2)

24 = 2 x 2 x 2 x 2 = 16 (Divide by 2)

23 = 2 x 2 x 2 = 8 (Divide by 2)

22 = 2 x 2 = 4 (Divide by 2)

21 = 1 x 2 = 2 (Divide by 2)

20 = 1.

As conclusion :

Remember, Anything raised to the zero power is 1.

a0 = b0 = 10 = 20 = all equal to 1.


    0 of 8192 characters used
    Post Comment
    • verdict profile image

      George Dimitriadis 

      7 months ago from Templestowe


      A informative treatment of indices with zero as the exponent. Perhaps your example with a camera's memory card using powers of 2 can be extended to a discussion of binary arithmetic in computers.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, 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:

    Show Details
    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 or domains, for performance and efficiency reasons. (Privacy Policy)
    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)
    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.
    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)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)