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1.2a Exponents. 1. Laws of Exponents. 2. Laws of Radicals. Exponents. Notation a n = a*a*a*a….*a, n times a 4 = a*a*a*a a 9 = a*a*a*a*a*a*a*a*a 3 4 = 3*3*3*3 = 81 ca n = c*a*a*a…*a, n times 13a 3 , where a =2 =13*2*2*2 =13*8 =104. Exponents. Laws of Exponents

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1.2a Exponents

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1 2a exponents

1.2a Exponents

1

Laws of Exponents

2

Laws of Radicals

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Exponents

Exponents

  • Notation

    • an = a*a*a*a….*a, n times

      • a4 = a*a*a*a

      • a9 = a*a*a*a*a*a*a*a*a

      • 34 = 3*3*3*3 = 81

    • can = c*a*a*a…*a, n times

    • 13a3, where a =2

      =13*2*2*2

      =13*8

      =104

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Exponents1

Exponents

  • Laws of Exponents

    • anam = an+m

      • 2329 = 23+9 = 212 = 4096

      • Note: the base number (a) must be the same

    • (am)n = amn

      • (23)4 = 23*4 = 212 = 4096

    • (ab)n = anbn

    • (a/b)n = an/bn

      • (2/5)3 = 23/53 = 8/125

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Exponents2

Exponents

  • Laws of Exponents (Cont.)

    • am/an = am-m

      • 25/23 = 25-3 = 22 = 4

    • a-m = 1/am

      • x-3 = 1/x3

    • a-m/b-n = bn/am

      • X-5/y-4 = y4/x5

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Radicals

Radicals

  • Notation:

    • Note:

  • Properties

    • if is a real number

      • ,

    • if a≥0

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Radicals1

Radicals

  • Laws of Radicals

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Practice problems

Practice Problems

  • Page 29

    Problems1-32

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