This document provides an overview of exponents and exponential notation: - Exponents show repeated multiplication, with the base being the factor and the exponent showing how many times the base is multiplied by itself. - Exponential notation compactly writes repeated multiplication, such as 2^6 representing 2 x 2 x 2 x 2 x 2 x 2. - Negative integers raised to an even power are positive, while raised to an odd power are negative. - A word problem example calculates 10^3 = 10 x 10 x 10 = 1,000. - Order of operations must be followed when evaluating expressions with exponents.

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 · 10 · 10 · 10 · 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 • 2 • 2 • 2 • 2 • 2 = 2 6 Exponential Notation Expanded Notation

4. Exponents…Show me! Exponential Notation. And Value. (The answer). a. 12 b. 6 x 6 c. –(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 • 6 = 36 The opposite of the quantity seven to the fourth power. -7 4 , - (7 • 7 • 7 • 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 • a • b • a • a = -2 • a • a • a • b = -2a 3 b

7. Exponents and Negative Integers So when you multiply 2 negative numbers… what do you get? A positive number When you multiply 3 negative numbers… 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 • 5 = 25 Multiplying/Dividing: 4 • 25 = 100. Addition/Subtraction?: Nope So, 100 is the answer.

12. Example Problem: -2x 3 + 4y, for x = -2 and y = 3. Substitute Variables: -2(-2) 3 + 4(3) Grouping Symbols: None Exponents: (-2) 3 = (-2)(-2)(-2) = -8 -2(-8)+ 4(3) Multiplication/Division: 16 + 12 = 28 Addition/Subtraction: None So, 28 is the answer.

13. Assignment #41: Page 180: 5 – 31 all. 32 and 33 are extra credit!!!