UNIT 6 DAY 1: PROPERTIES
OF EXPONENTS
Essential Questions: What are the properties of exponents?
How can we use these properties to simplify expressions?
VOCABULARY
•
•
•
Power: the result
of repeated
multiplication
Base: the number
being multiplied
Exponent: the
number of times to
repeat the
multiplication
base
3
4
power
4•4•4
64
exponen
t
EXPONENT PROPERTIES
Product of Like Bases
How? Keep the base, add the
exponents!
3
5
4 •4
8
4
WHY?
4•4•4•4•4•4•4•4
3
5
4
•
4
=
8
4
EXPONENT PROPERTIES
Quotient of Like Bases
How? Keep the base, subtract the
exponents!
6
5
4
=
5
2
5
6
5
WHY?
5•5•5•5•5•5
2
5
5•5
=
4
5
EXPONENT PROPERTIES
Power to a Power
How? Keep the base, multiply
the exponents!
2
4
(3 )
8
3
WHY?
2
2
2
2
8
3 •3 •3 •3
=3
3•3•3•3•3•3•3•3
EXPONENT PROPERTIES
Product to a Power
How? “Distribute” the exponent to each
factor!
3
(5x)
3
3
5x
3
125x
WHY?
3
5 • x • 5 • x • 5 • x = 125x
1
2
3
(5x) (5x) (5x)
EXPONENT PROPERTIES
Quotient to a Power
How? “Distribute” the exponent to the
numerator and denominator!
5
x
(y)
=
5
x
5
y
WHY?
x x x
x
x
•
•
•
•
y y y
y
y
=
5
x
5
y
EXPONENT PROPERTIES
Zero Exponent
How? Equals 1. Always.
0
24
=1
WHY? (click me)
EXPONENT PROPERTIES
Negative Exponent
How? Move the exponent
(reciprocal) to make it positive!
-3
4
1
3
4
WHY? (click me)
ractice: Simplify the exponential expressions.
2
x
7
5
x
20
a
a
( b)
7
a
7
b
6
y
3
(3x)
0
4
3
27x
1
•
3
y
3
y
3
x
5
4
(a )
ractice: Simplify the exponential expressions.
-3
2
1
3
2
4
4n
1
8
•
-6
2n
-2
8n
8
2
n
3
4
(2x )
3
(2x)
12
16x
3
8x
•
2
(4x)
•
2
16x
5
128x
3
4v
•
2
vu
4
2
4v u
3
2x
3
x
0
2x
2•1=2
SUMMARY
Essential Questions: What are the
properties of exponents? How can we
use these properties to simplify
expressions?
Take 1 minute to write 2 sentences
answering the essential questions.