Ch. 4, Sec 2: Exponents

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 =

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

Exponents: Exponential Notation
2 • 2 • 2 • 2 • 2 • 2 = 2 6
Exponential Notation Expanded Notation

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)

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

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

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

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.

Word Problem:
A microscope can magnify a specimen 10 3 times. How many times is that?

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.

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.

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.

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

Ch. 4, Sec 2: Exponents

by Middle School on Dec 01, 2009

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Ch. 4, Sec 2: Exponents — Presentation Transcript

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