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Using Properties of Exponents

Using Properties of Exponents. Properties of Exponents a&b are real numbers, m&n are integers. Product Property : a m * a n =a m+n Power of a Power Property : (a m ) n =a mn Power of a Product Property : (ab) m =a m b m Negative Exponent Property : a -m = ; a ≠0

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Using Properties of Exponents

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  1. Using Properties of Exponents

  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

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