## Learn about the rules of exponents v the following examples and also interactive exercises.You are watching: 5 to the 4th power in standard form In the table below, the number 2 is created as a factor repeatedly. The product of components is likewise displayed in this table. Suppose that her teacher asked girlfriend to Write 2 together a factor one million times for homework. Just how long do you think that would 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 element 5 times 2 x 2 x 2 x 2 x 2 x 2 = 64 2 is a variable 6 times 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128 2 is a variable 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 be a very time-consuming and also tedious task. A much better way to technique this is come use exponents. Exponential notation is an easier means to create a number together a product of numerous factors.

BaseExponent

The exponent tells united state how countless times the base is provided as a factor.

For example, to create 2 together a aspect one million times, the base is 2, and the exponent is 1,000,000. We compose this number in exponential kind as follows:

21,000,000

read as two increased to the millionth power 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 one more look in ~ 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 check numbers with a basic of 2. Let"s look in ~ some instances of composing exponents where the basic is a number various other than 2.

Example 2: Write 3 x 3 x 3 x 3 utilizing exponents, then read your answer aloud.

Solution: 3 x 3 x 3 x 3 = 34 3 increased to the 4th power

Example 3: Write 6 x 6 x 6 x 6 x 6 utilizing exponents, then read your prize 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 review your prize 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 form and in traditional 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 apply to numbers v exponents of 0, 1, 2 and also 3:

 Rule Example Any number (except 0) elevated to the zero power is equal to 1. 1490 = 1 Any number raised to the very first power is constantly equal to itself. 81 = 8 If a number is raised to the second power, we say that is squared. 32 is read as three squared If a number is elevated to the third power, we say it is cubed. 43 is check out as four cubed

Summary: Whole numbers deserve to be to express in conventional form, in factor form and in exponential form. Exponential notation provides it much easier to compose a number as a variable repeatedly. A number created in exponential kind is a base elevated to an exponent. The exponent tells united state how many times the base is supplied as a factor.

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### Exercises

Directions: read each concern below. Click as soon as in solution BOX and type in your answer; then click ENTER. Do not usage commas in your answers, just digits. After girlfriend click ENTER, a message will appear in the outcomes BOX to suggest whether your answer is correct or incorrect. To begin over, click CLEAR.