# Index Notation And The Zero Power Rule

Updated on August 17, 2019

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## 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.

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