extras 12 6 by HC120809065549

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									Lesson 12-6

Example 1 Multiply Powers
Find 33 · 3. Express using exponents.

33 · 3 = 33 · 31        3 = 31                    Check 33 · 3 = (3 · 3 · 3) · 3
      = 33 + 1          The common base is 3.                  =3·3·3·3
      = 34              Add the exponents.                     = 34 


Example 2 Multiply Monomials
Find –2x3(3x4). Express using exponents.

–2x3(3x4) = (–2 · 3)(x3 · x4)        Commutative and Associative Properties
          = (–6)(x3 + 4)             The common base is x.
          = –6x7                     Add the exponents.


Example 3 Divide Powers
    57
Find 3. Express using exponents.
    5

57    7–3
53 = 5                  The common base is 5.
   = 54                 Simplify.


Example 4 Divide Powers
    m10
Find 2 . Express using exponents.
    m

m10    10 – 2
m2 = m                  The common base is m.
    = m8                Simplify.
Example 5 Divide powers to Solve a Problem
SCIENCE A petri dish contains 105 bacteria after one hour. After four hours, there are
1010 bacteria in the dish. How many times more bacteria are in the dish at four hours than
at one hour?

To find how many times more bacteria, divide 1010 by 105.

1010     10 – 5
105 = 10             Quotient of Powers
     = 105           Simplify.

The number of bacteria from one hour to four hours is 105 times as much.

								
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