Learn around the rule of exponents with the complying with examples and interactive exercises.
You are watching: What is the number expressed using exponents
In the table below, the number 2 is composed as a factor repeatedly. The product of factors is likewise displayed in this table. Suppose that your teacher asked girlfriend to Write 2 as a factor one million times for homework. How long perform you think that would certainly take? Answer.
| Factors | Product that Factors | Description |
| 2 x 2 = | 4 | 2 is a variable 2 times |
| 2 x 2 x 2 = | 8 | 2 is a aspect 3 times |
| 2 x 2 x 2 x 2 = | 16 | 2 is a factor 4 times |
| 2 x 2 x 2 x 2 x 2 = | 32 | 2 is a variable 5 times |
| 2 x 2 x 2 x 2 x 2 x 2 = | 64 | 2 is a element 6 times |
| 2 x 2 x 2 x 2 x 2 x 2 x 2 = | 128 | 2 is a aspect 7 times |
| 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = | 256 | 2 is a element 8 times |
Writing 2 as a variable one million times would certainly be a very time-consuming and tedious task. A far better way to technique this is come use exponents. Exponential notation is one easier means to write a number together a product of countless factors.
BaseExponent
The exponent tells us how countless times the base is offered as a factor.
For example, to create 2 as a aspect one million times, the base is 2, and the exponent is 1,000,000. We write this number in exponential kind as follows:
21,000,000
read as two elevated to the millionth power
Solution: 2 x 2 x 2 x 2 x 2 = 25 2 raised to the fifth power
Let us take one more look at the table from above to see just how exponents work.
| ExponentialForm | FactorForm | StandardForm |
| 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 |
| 26 = | 2 x 2 x 2 x 2 x 2 x 2 = | 64 |
| 27 = | 2 x 2 x 2 x 2 x 2 x 2 x 2 = | 128 |
| 28 = | 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = | 256 |
So far we have only examined numbers v a basic of 2. Let"s look in ~ some examples of composing exponents whereby the basic is a number other than 2.
Example 2: Write 3 x 3 x 3 x 3 utilizing exponents, then check out your answer aloud.
Solution: 3 x 3 x 3 x 3 = 34 3 increased to the fourth power
Example 3: Write 6 x 6 x 6 x 6 x 6 utilizing exponents, then review your answer aloud.
Solution: 6 x 6 x 6 x 6 x 6 = 65 6 increased to the 5th power
Example 4: Write 8 x 8 x 8 x 8 x 8 x 8 x 8 utilizing exponents, then read your prize aloud.
Solution: 8 x 8 x 8 x 8 x 8 x 8 x 8 = 87 8 raised to the seventh power
Example 5: Write 103, 36, and also 18 in factor type and in standard form.
Solution:
| ExponentialForm | FactorForm | StandardForm |
| 103 | 10 x 10 x 10 | 1,000 |
| 36 | 3 x 3 x 3 x 3 x 3 x 3 | 729 |
| 18 | 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 | 1 |
The complying with rules use to numbers through exponents of 0, 1, 2 and 3:
| Rule | Example |
| Any number (except 0) increased to the zero strength is same to 1. | 1490 = 1 |
| Any number increased to the first power is constantly equal to itself. | 81 = 8 |
| If a number is raised to the second power, us say it is squared. | 32 is read as three squared |
| If a number is raised to the third power, us say the is cubed. | 43 is read as four cubed |
Summary: Whole numbers have the right to be express in traditional form, in factor kind and in exponential form. Exponential notation provides it simpler to compose a number as a element repeatedly. A number created in exponential form is a base increased to an exponent. The exponent tells us how countless times the base is provided as a factor.
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Exercises
Directions: review each inquiry below. Click when in an answer BOX and kind in her answer; then click ENTER. Perform not use commas in your answers, simply digits. After friend click ENTER, a blog post will show up in the results BOX to indicate whether her answer is exactly or incorrect. To begin over, click CLEAR.