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Understanding Exponent Properties: Comprehensive Guide and Examples

This guide covers the essential properties of exponents with clear definitions and examples. You'll explore the Product Property, Power of a Power Property, Power of a Product Property, Negative Exponent Property, Zero Exponent Property, Quotient of Powers, and Power of Quotient, all of which are crucial for simplifying expressions in algebra. Through detailed examples, such as calculations involving negative and zero exponents, you'll gain a deeper understanding of how to manipulate exponents effectively. Ideal for students looking to strengthen their math skills.

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Understanding Exponent Properties: Comprehensive Guide and Examples

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  1. 6.1 Using Properties of Exponents p. 323

  2. Properties of Exponentsa&b are real numbers, m&n are integers • Product Property: am * an=am+n • Power of a Power Property: (am)n=amn • Power of a Product Property: (ab)m=ambm • Negative Exponent Property: a-m= ; a≠0 • Zero Exponent Property: a0=1; a≠0 • Quotient of Powers: am= am-n;a≠0 an • Power of Quotient: b≠0

  3. Example 1 – Product Property • (-5)4 * (-5)5 = • (-5)4+5 = • (-5)9 = • -1953125

  4. Example 2 • x5 * x2 = • x5+2 = • x7

  5. Example 3 – Power of a Power • (23)4 = • 23*4 = • 212 = • 4096

  6. Example 4 • (34)2 = • 34*2 = • 38 = • 6561

  7. Example 5 – Neg. Exponent • (-5)-6(-5)4 = • (-5)-6+4 = • (-5)-2 =

  8. Example 6 – Quotient of Powers

  9. Example 7 – Power of Quotient

  10. Example 8 – Zero Exponent • (7b-3)2 b5 b = • 72 b-3*2 b5 b = • 49 b-6+5+1 = • 49b0 = • 49

  11. Example 9 – Quotient of Powers

  12. Scientific Notation • 131,400,000,000= 1.314 x 1011 Put that number here! Move the decimal behind the 1st number How many places did you have to move the decimal?

  13. 131,400,000,000 = 5,284,000 1.314 x 1011= 5.284 x 106 Example – Scientific Notation

  14. Assignment

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