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.

FactorsProduct that FactorsDescription
2 x 2 =42 is a variable 2 times
2 x 2 x 2 =82 is a aspect 3 times
2 x 2 x 2 x 2 =162 is a factor 4 times
2 x 2 x 2 x 2 x 2 =322 is a variable 5 times
2 x 2 x 2 x 2 x 2 x 2 =642 is a element 6 times
2 x 2 x 2 x 2 x 2 x 2 x 2 =1282 is a aspect 7 times
2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 =2562 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

*
Example 1: Write 2 x 2 x 2 x 2 x 2 making use of exponents, then check out your price aloud.

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.

ExponentialFormFactorFormStandardForm
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: 

ExponentialFormFactorFormStandardForm
10310 x 10 x 101,000
363 x 3 x 3 x 3 x 3 x 3729
181 x 1 x 1 x 1 x 1 x 1 x 1 x 11

The complying with rules use to numbers through exponents of 0, 1, 2 and 3:

RuleExample
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.

See more: Why Did Reggie Bush And Kim Break Up, Why Kim Kardashian & Reggie Bush Really Broke Up!

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.