Reading and Evaluating Numbers in Exponential Form
Larn virtually the rules of exponents with the following examples and interactive exercises.
In the table below, the number ii is written as a factor repeatedly. The production of factors is also displayed in this table. Suppose that your instructor asked yous toWrite 2 as a gene one million times for homework. How long do y'all retrieve that would take? Answer.
| Factors | Product of Factors | Description |
| 2 x 2 = | four | 2 is a factor 2 times |
| 2 10 2 10 ii = | 8 | 2 is a factor 3 times |
| 2 ten two 10 two x 2 = | 16 | two is a factor iv times |
| 2 x two x ii x 2 x 2 = | 32 | 2 is a factor five times |
| 2 x 2 x ii x ii x 2 x 2 = | 64 | 2 is a cistron 6 times |
| two x 2 x two 10 two 10 2 x two x 2 = | 128 | two is a factor 7 times |
| 2 ten two x 2 x 2 x 2 x 2 x 2 x ii = | 256 | 2 is a factor 8 times |
Writing two as a gene one million times would be a very time-consuming and deadening chore. A better way to approach this is to utiliseexponents. Exponential notation is an easier way to write a number as a production of many factors.
Base Exponent
Theexponent tells us how many times thebase is used as a gene.
For example, to write 2 equally a factor one one thousand thousand times, the base is ii, and the exponent is i,000,000. Nosotros write this number in exponential form equally follows:
2 i,000,000
read as2 raised to the millionth power
Example i: Write 2 x two x 2 10 2 x 2 using exponents, and then read your answer aloud.
Solution: two x 2 x 2 x 2 10 2 = 25 ii raised to the 5th power
Let us take another look at the tabular array from higher up to run across how exponents piece of work.
| Exponential Grade | Cistron Form | Standard Course |
| 22 = | 2 x two = | 4 |
| 23 = | ii x 2 x two = | viii |
| ii4 = | 2 x 2 ten 2 x 2 = | 16 |
| 25 = | 2 x 2 x 2 ten 2 10 2 = | 32 |
| 26 = | 2 x 2 x 2 10 2 ten 2 x ii = | 64 |
| 2seven = | 2 x 2 10 two x 2 10 2 x 2 x 2 = | 128 |
| ii8 = | ii x 2 x ii x two x ii x 2 x 2 x 2 = | 256 |
And so far we have only examined numbers with a base of 2. Let's look at some examples of writing exponents where the base is a number other than 2.
Example two: Write 3 x three ten 3 x 3 using exponents, then read your answer aloud.
Solution: 3 x 3 x iii x 3 = 34 three raised to the quaternary power
Example 3: Write vi x 6 x vi ten 6 x 6 using exponents, then read your answer aloud.
Solution: half-dozen x half-dozen x 6 x six ten 6 = 6five 6 raised to the fifth power
Example iv: Write viii ten eight x eight x 8 x 8 x viii x viii using exponents, so read your answer aloud.
Solution: 8 ten 8 x 8 10 eight 10 8 x 8 10 8 = viii7 8 raised to the seventh ability
Example five: Write tenthree, iii6, and 18 in factor grade and in standard form.
Solution:
| Exponential Form | Cistron Class | Standard Form |
| 103 | 10 ten x ten 10 | 1,000 |
| 36 | 3 10 3 ten three ten 3 ten 3 x 3 | 729 |
| one8 | 1 ten 1 x 1 ten 1 x 1 x i x 1 x 1 | 1 |
The post-obit rules apply to numbers with exponents of 0, 1, 2 and iii:
| Dominion | Example |
| Whatsoever number (except 0) raised to the zilch power is equal to 1. | 1490 = one |
| Whatsoever number raised to the get-go power is always equal to itself. | eight1 = 8 |
| If a number is raised to the second ability, we say it issquared. | 32 is read equallyiii squared |
| If a number is raised to the third power, we say information technology iscubed. | 43 is read every bit4 cubed |
Summary: Whole numbers tin can be expressed in standard form, in gene form and in exponential course. Exponential note makes it easier to write a number equally a factor repeatedly. A number written in exponential form is a base of operations raised to an exponent. The exponent tells united states of america how many times the base is used equally a factor.
Exercises
Directions: Read each question below. Click once in an ANSWER BOX and type in your reply; and so click ENTER. Do not employ commas in your answers, simply digits. After you click ENTER, a message will announced in the RESULTS BOX to indicate whether your reply is correct or incorrect. To start over, click Clear.
| ane. | Write 4five in standard form. |
| 2. | Write 54 in standard form. |
| 3. | What is 500,000,000 raised to the zero power? |
| 4. | What is 237 raised to the offset power? |
| five. | The number 81 is 3 raised to which ability? |
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Source: https://www.mathgoodies.com/lessons/vol3/exponents
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