Learn around the rule of exponents v the following examples and also interactive exercises.

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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.

FactorsProduct the FactorsDescription
2 x 2 =42 is a variable 2 times
2 x 2 x 2 =82 is a factor 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 aspect 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 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

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Example 1: Write 2 x 2 x 2 x 2 x 2 using exponents, then review your answer aloud.

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.

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 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: 

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 that 0, 1, 2 and 3:

RuleExample
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.