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# Ch. 4, Sec 2: Exponents

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Chapter 4, Section 2 Notes on Exponents

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### Ch. 4, Sec 2: Exponents

1. 1. Ch. 4, Sec 2: Exponents <ul><li>Warm Up: Find the Product </li></ul><ul><li>3 x 3 x 3 x 3 = </li></ul><ul><li>-12 x (-12) = </li></ul><ul><li>(-4)(-4)(-4)(-4) = </li></ul><ul><li>10 · 10 · 10 · 10 · 10 = </li></ul>
2. 2. Exponents <ul><li>You can use EXPONENTS to show repeated multiplication. </li></ul><ul><li>(Just like multiplication can show repeated addition). </li></ul><ul><li>A POWER has two parts : </li></ul><ul><li>A BASE : the factor. (a number or variable) </li></ul><ul><li>And an EXPONENT : the number of times the base (or factor) is multiplied by itself. </li></ul>9 7 Base Exponent
3. 3. Exponents: Exponential Notation <ul><li>2 • 2 • 2 • 2 • 2 • 2 = 2 6 </li></ul>Exponential Notation Expanded Notation
4. 4. Exponents…Show me! <ul><li>Exponential Notation. </li></ul><ul><li>And Value. (The answer). </li></ul><ul><li>a. 12 </li></ul><ul><li>b. 6 x 6 </li></ul><ul><li>c. –(7 x 7 x 7) </li></ul><ul><li>d. (-8)(-8)(-8)(-8)(-8) </li></ul>
5. 5. Exponential Notation and Answers <ul><li>Twelve to the first power. </li></ul><ul><li>12 1 , 12 </li></ul><ul><li>Six to the second power, or six squared. </li></ul><ul><li>6 2 , 6 • 6 = 36 </li></ul><ul><li>The opposite of the quantity seven to the fourth power. </li></ul><ul><li>-7 4 , - (7 • 7 • 7 • 7) 4 = - (2,401) = -2,401 </li></ul><ul><li>Negative eight to the fifth power. </li></ul><ul><li>(-8) 5 , (-8)(-8)(-8)(-8)(-8) = -32,768 </li></ul>
6. 6. Writing Exponential Notation <ul><li>Remember to include the Negative Sign. </li></ul><ul><li>(-5)(-5)(-5) = (-5) 3 </li></ul><ul><li>Rewrite the expression using the commutative and associative properties. </li></ul><ul><li>-2 • a • b • a • a = </li></ul><ul><li>-2 • a • a • a • b = -2a 3 b </li></ul>
7. 7. Exponents and Negative Integers <ul><li>So when you multiply 2 negative numbers… what do you get? </li></ul><ul><li>A positive number </li></ul><ul><li>When you multiply 3 negative numbers… what do you get? </li></ul><ul><li>A negative number </li></ul>
8. 8. Exponents and Negative Numbers <ul><li>When you multiply an EVEN number of negative integers, the answer will be positive. </li></ul><ul><li>When you multiply an ODD number of negative integers, the answer will be negative. </li></ul>
9. 9. Word Problem: <ul><li>A microscope can magnify a specimen 10 3 times. How many times is that? </li></ul>
10. 10. Orders of Operations <ul><li>Work inside the grouping symbols </li></ul><ul><li>Simplify any terms with exponents. </li></ul><ul><li>Multiply and divide in order from left to right. </li></ul><ul><li>Add and subtract in order from left to right. </li></ul>
11. 11. Example Problem: <ul><li>4(3+2) 2 = </li></ul><ul><li>Grouping Symbols: 3+2 = 5 </li></ul><ul><li>Exponents: 5 2 = 5 • 5 = 25 </li></ul><ul><li>Multiplying/Dividing: 4 • 25 = 100. </li></ul><ul><li>Addition/Subtraction?: Nope </li></ul><ul><li>So, 100 is the answer. </li></ul>
12. 12. Example Problem: <ul><li>-2x 3 + 4y, for x = -2 and y = 3. </li></ul><ul><li>Substitute Variables: -2(-2) 3 + 4(3) </li></ul><ul><li>Grouping Symbols: None </li></ul><ul><li>Exponents: (-2) 3 = (-2)(-2)(-2) = -8 </li></ul><ul><li> -2(-8)+ 4(3) </li></ul><ul><li>Multiplication/Division: 16 + 12 = 28 </li></ul><ul><li>Addition/Subtraction: None </li></ul><ul><li>So, 28 is the answer. </li></ul>
13. 13. Assignment #41: <ul><li>Page 180: 5 – 31 all. </li></ul><ul><li>32 and 33 are extra credit!!! </li></ul>
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