Exponent Laws

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Exponent Laws
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Laws of Exponents

• Whenever we have variables which contain
  exponents with the same bases, we can do
  mathematical operations with them. These are
  called the Exponents Laws.
• bx
• b the base x the exponent

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Other Properties of Exponents

• Any single number or variable is always to the
  power of one (1)
• If you have a negative exponent , you use the
  reciprocal of the base. Notice ,your exponent
  will then be positive.

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Multiplying Powers with the SAME Base

• Product of a Power
• When you multiply a power with the same base, you
  add the exponents.
• am x an a mn a is the base
  and m and n are the exponents.
• You need to show your work in the following
  format.
• 23 x 24 2 (34) 2 7

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Dividing Powers with the Same Base
Quotient of Powers When you divide powers with
the same base, you subtract the exponents. a4
a3 a 4- 3 24 23 2 (4- 3) 21

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Raising a Power

• Power of a Power
• When you are raising a power by an exponent, you
  must, multiply the exponents.
• (a m)n a (m x n)
  
• (23)4 2 (3 x 4) 212

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Power of a Product

• When you are finding a power of a product , each
  number in the brackets is affected.
• (ab)m ambm
• ( when there is no sign , remember that the
  operation is multiplication
• SO ab is a times b)
• ( 3 x 6 )3 33 x 63
• 183 27 x 216
• 5832 5832

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Power of a Product contd

• The opposite is also important.
• If you have 45 x 65 , notice that the
  exponents are the SAME.
• You can now do the opposite . For example, you
  can now take the exponent from the problem and
  multiply the bases. Then you can use your
  exponent.
• ( 4 x 6 ) 5 which is 245

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• Power of a Quotient
• When you have a fraction, the exponent affects
  both the numerator AND the denominator.

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Combining Operations

• If you have more than one operation to do , you
  will need to use your BEDMAS rules.
• (45 ? 64)5 ? (4 ? 63)6
• (45)5 x (64)5 ? 46 x (63)6
• 4(25-6) X 6
  (20 -18)
• 4 19 x 62