## Learn about the rules 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 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.