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Laws of Exponents

Laws of Exponents. Vocabulary. Factor: an integer that divides into another integer with no remainder. 24. 1, 2, 3, 4, 6, 8, 12, 24. Exponent: tells how many times to multiply a number by itself Base: the number that is multiplied by itself

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Laws of Exponents

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  1. Laws of Exponents

  2. Vocabulary • Factor: an integer that divides into another integer with no remainder. 24 1, 2, 3, 4, 6, 8, 12, 24

  3. Exponent: tells how many times to multiply a number by itself • Base: the number that is multiplied by itself • Power: an expression using a base and an exponent 45 = 4 • 4 • 4 • 4 • 4 2 6 63

  4. Expressions with Exponents (-6)• (-6)• (-6)• (-6) • (-6)4 36 • 36 1,296 • -64 -(6)• (6)• (6)• (6) -(36 • 36) -1,296 *They are not the same.

  5. Exponents and Multiplication To Multiply powers with the SAME base: **Add the exponents and keep the base** Examples: 1) 32∙ 36 = 38 2) am ∙ an = am + n

  6. Exponents and Division To Divide powers with the SAME base: **Subtract the exponents and keep the base** Examples: 1) 8 5 = 8 2 8 3 2) a m = a m - n a n

  7. Zero as an Exponent • For any non-zero number a, a 0 = 1 • Examples: 1) 9 0 = 1 2) 15 0 = 1 3) 1 0 = 1

  8. Negative Exponents • For any non-zero number a and integer n, a –n = 1 an Example: 8 -5 = 1 85

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