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In this chapter, you will learn about the short cuts to writing . This is known as writing a number in exponential notation .
Exponential notation is a short way of writing the same number multiplied by itself many times. For example, instead of , we write to show that the number 5 is multiplied by itself 3 times and we say “5 to the power of 3”. Likewise is and is . We will now have a closer look at writing numbers using exponential notation.
Exponential notation means a number written like
where is an integer and can be any real number. is called the base and is called the exponent or index .
The th power of is defined as:
with multiplied by itself times.
We can also define what it means if we have a negative exponent . Then,
If is an even integer, then will always be positive for any non-zero real number . For example, although is negative, is positive and so is .
Khan academy video on exponents - 1
Khan academy video on exponents-2
There are several laws we can use to make working with exponential numbers easier. Some of these laws might have been seen in earlier grades, but we will list all the laws here for easy reference and explain each law in detail, so that you can understand them and not only remember them.
Our definition of exponential notation shows that
For example, and .
Khan academy video on exponents - 3
Our definition of exponential notation shows that
For example,
Our definition of exponential notation for a negative exponent shows that
This means that a minus sign in the exponent is just another way of showing that the whole exponential number is to be divided instead of multiplied.
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