## Learn about the rules of exponents with the complying with examples and interactive exercises.

You are watching: Write using exponents. (–4)(–4)

In the table below, the number 2 is created 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 variable one million times for homework. How long do you think that would take? Answer.

Factors | Product of Factors | Description |

2 x 2 = | 4 | 2 is a factor 2 times |

2 x 2 x 2 = | 8 | 2 is a aspect 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 aspect 5 times |

2 x 2 x 2 x 2 x 2 x 2 = | 64 | 2 is a aspect 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 aspect 8 times |

Writing 2 together a element one million times would be a really time-consuming and tedious task. A better way to technique this is come use **exponents**. Exponential notation is one easier means to compose a number together a product of countless factors.

BaseExponent

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

For example, to create 2 together a element one million times, the basic is 2, and the exponent is 1,000,000. We compose this number in exponential form 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 us take one more look at the table from above to see exactly 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 actually only check numbers with a basic of 2. Let"s look in ~ some instances of creating exponents whereby the base is a number various other than 2.

Example 2: Write 3 x 3 x 3 x 3 using exponents, then review 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 check out your answer aloud.

Solution: 6 x 6 x 6 x 6 x 6 = 65 6 elevated to the 5th power

Example 4: Write 8 x 8 x 8 x 8 x 8 x 8 x 8 using exponents, then read your prize aloud.

Solution: 8 x 8 x 8 x 8 x 8 x 8 x 8 = 87 8 elevated to the saturday power

Example 5: Write 103, 36, and 18 in factor kind and in conventional 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 adhering to rules apply to numbers with exponents of 0, 1, 2 and 3:

Rule | Example |

Any number (except 0) raised to the zero power is equal to 1. | 1490 = 1 |

Any number raised to the an initial power is always equal to itself. | 81 = 8 |

If a number is elevated to the second power, we say it is squared. | 32 is check out as three squared |

If a number is elevated to the 3rd power, us say that is cubed. | 43 is check out as four cubed |

Summary: Whole numbers have the right to be to express in conventional form, in factor form and in exponential form. Exponential notation makes it easier to create a number together a element repeatedly. A number composed in exponential type is a base increased to one exponent. The exponent tells us how countless times the basic is offered as a factor.

See more: Is It Legal To Kick Your Child Out At 18 Year Old? In California Law

**Exercises**

Directions: review each inquiry below. Click when in an answer BOX and kind in her answer; climate click ENTER. Execute not usage commas in your answers, just digits. After you click ENTER, a message will show up in the outcomes BOX to show whether her answer is exactly or incorrect. To begin over, click CLEAR.