Source: Clipboard/Lined Paper, algotruneman, Open Clipart

In this section, you will review numerical expressions that include exponents and prime factorization.

Click on the boxes below to review factorization terms.

Use the interactive below to review and practice exponents and prime factorization. Match cards that have equivalent expressions.

Using the information from the interactive above, answer the following questions:

• Which pairs of numbers are prime numbers and which pairs are composite numbers?

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  Need a hint?

  Prime numbers have only factors of 1 and themselves. Composite numbers have factors other than 1 and themselves.
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  Check Your Answer

  All of the pairs are composite numbers. They all include factors other than 1 and themselves.
• Explain why the prime factorizations used exponents.

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  What do exponents represent?
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  Exponents can be viewed as a short cut to writing out all the factors. For example: 72 = 2³ × 3² can also be written as 72 = 2 × 2 × 2 × 3 × 3. It is easier and shorter to write the prime factorization of 72 with exponents.

Practice

1. Find the prime factorization for each number.
2. Write it in exponential notation if possible.

1. 300

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   Need a hint?

   Since 0 is the unit digit, 300 is divisible by 10.
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   Check Your Answer

   300 = 2 × 2 × 3 × 5 × 5
   300 = 2² × 3 × 5²
2. 195

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   Need a hint?

   Since 5 is the unit digit, 195 is divisible by 5.
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   Check Your Answer

   195 = 3 × 5 × 13
   Since there is one of each factor, this cannot be written with exponents.
3. 693

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   Need a hint?

   Add the digits together. Their sum is divisible by 3, therefore, 693 is divisible by 3.
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   Check Your Answer

   693 = 3 × 3 × 7 × 11 = 3² × 7 × 11
4. 357

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   Need a hint?

   Add the digits together to see if their sum is divisible by 3.
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   Check Your Answer

   357 = 3 × 7 × 17
   Since there is one of each factor, this cannot be written with exponents.