Download Exponent PreSkills

Introduction to Exponents
Pre-Skills for 2.1
Basic Definitions
Exponent:
Tells how many times a base is used in a factor
Base
The number or variable that undergoes repeated
multiplication
Example
24 = 2 • 2 • 2 • 2 = 16
Important Examples
 -34 =
 (-3)3 =
- (3 • 3 • 3 • 3)
-1 (9 • 9 ) = -81
 (-3)4 =
-3 • -3 • -3 • -3 =
9
•
9=
81
 -33 = - (3 • 3 • 3 )
-1 (27) = -27
-3 • -3 • -3 =
9 • -3 = -27
 x5 = x • x • x • x • x
 y3= y • y • y
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
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
Exponents with Fractions
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
example
2 2
 ( )
3
 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
example
1 4
 ( )
2
 Write out the fraction four times
1

2
1
2
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=
1
16