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# Ch. 4, Sec 2: Exponents

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Chapter 4, Section 2 Notes on Exponents

Chapter 4, Section 2 Notes on Exponents

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### Transcript

• 1. Ch. 4, Sec 2: Exponents
• Warm Up: Find the Product
• 3 x 3 x 3 x 3 =
• -12 x (-12) =
• (-4)(-4)(-4)(-4) =
• 10 Â· 10 Â· 10 Â· 10 Â· 10 =
• 2. Exponents
• You can use EXPONENTS to show repeated multiplication.
• (Just like multiplication can show repeated addition).
• A POWER has two parts :
• A BASE : the factor. (a number or variable)
• And an EXPONENT : the number of times the base (or factor) is multiplied by itself.
9 7 Base Exponent
• 3. Exponents: Exponential Notation
• 2 â€¢ 2 â€¢ 2 â€¢ 2 â€¢ 2 â€¢ 2 = 2 6
Exponential Notation Expanded Notation
• 4. Exponentsâ€¦Show me!
• Exponential Notation.
• And Value. (The answer).
• a. 12
• b. 6 x 6
• c. â€“(7 x 7 x 7)
• d. (-8)(-8)(-8)(-8)(-8)
• 5. Exponential Notation and Answers
• Twelve to the first power.
• 12 1 , 12
• Six to the second power, or six squared.
• 6 2 , 6 â€¢ 6 = 36
• The opposite of the quantity seven to the fourth power.
• -7 4 , - (7 â€¢ 7 â€¢ 7 â€¢ 7) 4 = - (2,401) = -2,401
• Negative eight to the fifth power.
• (-8) 5 , (-8)(-8)(-8)(-8)(-8) = -32,768
• 6. Writing Exponential Notation
• Remember to include the Negative Sign.
• (-5)(-5)(-5) = (-5) 3
• Rewrite the expression using the commutative and associative properties.
• -2 â€¢ a â€¢ b â€¢ a â€¢ a =
• -2 â€¢ a â€¢ a â€¢ a â€¢ b = -2a 3 b
• 7. Exponents and Negative Integers
• So when you multiply 2 negative numbersâ€¦ what do you get?
• A positive number
• When you multiply 3 negative numbersâ€¦ what do you get?
• A negative number
• 8. Exponents and Negative Numbers
• When you multiply an EVEN number of negative integers, the answer will be positive.
• When you multiply an ODD number of negative integers, the answer will be negative.
• 9. Word Problem:
• A microscope can magnify a specimen 10 3 times. How many times is that?
• 10. Orders of Operations
• Work inside the grouping symbols
• Simplify any terms with exponents.
• Multiply and divide in order from left to right.
• Add and subtract in order from left to right.
• 11. Example Problem:
• 4(3+2) 2 =
• Grouping Symbols: 3+2 = 5
• Exponents: 5 2 = 5 â€¢ 5 = 25
• Multiplying/Dividing: 4 â€¢ 25 = 100.