Exponents

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Exponents

• Not so EXTRATERRESTRIAL

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For each of the following, can you identify the
base and the exponent?

• 1. 47
• 2. 1110
• 3. 1002
• If a number doesnt have an exponent, then you
  can always assume the exponent is 1
• Ex 771

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Vocab

• Polynomial-
• Monomial-
• Constant-
• Coefficient-
• Zero exponent-
• Negative exponent-

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Polynomial

• An algebraic expression consisting of variables,
  coefficients, and constants, involving only the
  operations of addition, subtraction,
  multiplication and non negative whole exponents
• Examples
• 6x4
• 15h-17h2
• m32m24

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Monomial-

• A single algebraic term
• May be.
• A constant
• A variable
• A product of a constant and a variable

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Laws of Exponents

• Product (multiplication) of Powers
• (am)(an) amn
• Multiply the coefficients, ADD the exponents!
• Example 1 x5x2

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ADD the exponents!

• Example 2 x3y-2
• Example 3 (5x4y8)(3x-3y)

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Practice!

• 1) k4k-2k3
• 2) h7g-1h5
• 3) (2a3b4c-5)(4ab-8)

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TIC TAC TOE!
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Laws of Exponents

• Power of a Power
• (am)n amn
• MULTIPLY the exponents!
• Example 1 (x5)-2

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More Examples!

• Example 2 (x3)3
• Example 3 (y8)-4

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Practice!

• 1) (k4)8
• 2) (g-1)5
• 3) (c-5)-2

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Power of Power with more than one number,
variable, etc

• (4x)2 requires that you distribute the 2 to the 4
  and the x
• 42x2

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Try these!

• (gm)6
• (4w3)3

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Sometimes you have to use both

• What if you have (2v)2(2v)
• First distribute the power outside the
  parentheses to the info inside
• Then use what we learned about adding exponents
  and multiplying coefficients

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Try this(ba4)(2ba4)3
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Dividing Exponents

•  

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More examples

•  

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Negative Exponents

• Bottom line We dont like em!
• So how do we get rid of em?
• Move them

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Negative Exponents
Any number except 0 with a negative exponent
equals its reciprocal with the opposite exponent.
 
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Evaluating Negative Exponents

• Write the reciprocal, change the sign of the
  exponent
• Simplify