1. Introduction to Exponents
Pre-Skills for 2.1

2. Basic Definitions Exponent:
Tells how many times a base is used in a factor
Base
The number or variable that undergoes repeated multiplication
Example = 2 • 2 • 2 • 2 = 16

3. Important Examples -34 = - (3 • 3 • 3 • 3) -1 (9 • 9 ) = -81 (-3)4 =
- (3 • 3 • 3 • 3)
-1 (9 • 9 ) = -81
(-3)4 =
-3 • -3 • -3 • -3 =
• =
-33 = - (3 • 3 • 3 )
-1 (27) = -27
(-3)3 =
-3 • -3 • -3 =
9 • = -27
x5 = x • x • x • x • x
y3= y • y • y

4. Reminders on Evaluating Exponents
A base with an exponent of zero equals 1
10 0 = 1
25,000 0 =1
A base with an exponent of 1 equals the base
51 = 5
1,000 1 =1,000

5. Reminders
A positive base with a even exponent equals a positive answer
Example 52= 5 • 5 = 25
A negative base with an even exponent equals a positive answer:
Example: (-3)2 = (-3) • (-3) = 9
A negative with an odd exponent equals a negative answer
Example: (-2)3= (-2)(-2)(-2) = -8
A base with a negative sign in front equals a negative answer
Example: -23= -(2 • 2 • 2) = -8
Example: -92= - (9 •9)= -81

6. Exponents with Fractions

7. When exponents are on fractions
The fraction is the base
Write out the fraction as many times as decided by the exponent
Multiply the numerator
Multiply the denominator
Final answer

8. example ( 2 3 )2 Write out the fraction twice 2 3 x 2 3
Multiply the numerator 2 x 2 = 4
Multiply the denominator 3 x 3 =9
Final Answer= 4 9

9. example ( 1 2 )4 Write out the fraction four times
1 2 x x x 1 2
Multiply the numerator 1 x 1 x 1 x 1 =1
Multiply the denominator 2 x 2 x 2 x 2 = 16
Final Answer=