Learn around the rule of exponents v the following examples and also interactive exercises.
You are watching: How do you write an exponent in standard form
In the table below, the number 2 is created as a factor repeatedly. The product of factors is also displayed in this table. Suppose that your teacher asked you to Write 2 together a aspect one million times for homework. Just how long perform you think that would certainly take? Answer.
| Factors | Product the Factors | Description |
| 2 x 2 = | 4 | 2 is a variable 2 times |
| 2 x 2 x 2 = | 8 | 2 is a factor 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 aspect 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 aspect 8 times |
Writing 2 as a element one million times would certainly be a really time-consuming and also tedious task. A much better way to technique this is come use exponents. Exponential notation is an easier method to write a number together a product of numerous factors.
BaseExponent
The exponent tells us how countless times the base is supplied as a factor.
For example, to create 2 together a aspect one million times, the basic is 2, and also the exponent is 1,000,000. We create this number in exponential kind as follows:
21,000,000
read as two raised to the millionth power
Solution: 2 x 2 x 2 x 2 x 2 = 25 2 increased to the 5th power
Let united state take another look in ~ the table from over 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 much we have actually only examined numbers with a base of 2. Let"s look at some instances of writing exponents wherein the basic is a number various other than 2.
Example 2: Write 3 x 3 x 3 x 3 utilizing exponents, then check out your price aloud.
Solution: 3 x 3 x 3 x 3 = 34 3 raised to the fourth power
Example 3: Write 6 x 6 x 6 x 6 x 6 utilizing exponents, then check out your prize aloud.
Solution: 6 x 6 x 6 x 6 x 6 = 65 6 raised to the fifth power
Example 4: Write 8 x 8 x 8 x 8 x 8 x 8 x 8 making use of exponents, then review your price aloud.
Solution: 8 x 8 x 8 x 8 x 8 x 8 x 8 = 87 8 increased to the saturday power
Example 5: Write 103, 36, and 18 in factor kind and in conventional 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 that 0, 1, 2 and 3:
| Rule | Example |
| Any number (except 0) increased to the zero strength is equal to 1. | 1490 = 1 |
| Any number increased to the an initial power is always equal come itself. | 81 = 8 |
| If a number is raised to the 2nd power, we say that is squared. | 32 is check out 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 expressed in conventional form, in factor kind and in exponential form. Exponential notation renders it simpler to write a number as a factor repeatedly. A number composed in exponential kind is a base increased to one exponent. The exponent tells us how numerous times the base is offered as a factor.
See more: How Much Does A Gallon Of Gasoline Weight Per Gallon? Produce 20 Pounds Of Carbon Dioxide
Exercises
Directions: check out each question below. Click when in solution BOX and form in her answer; climate click ENTER. Carry out not usage commas in your answers, just digits. After friend click ENTER, a article will appear in the outcomes BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.