Lesson 1.3 (8)

Course 3, Lesson 1-3
Write each expression using exponents.
1.
2.
3.
Evaluate each expression.
4.
5.
6. Write
using exponents.
• • • • • • • •c c c c c c c c c
8 • 8 • 8 • 8 • 8
1 1
2 2
• • • • x • • • • • •x y x y x x x y
9
2
3
6
• • • • • • • • • •m n m p m n m p n m p

ANSWERS
1. c9
2. 85
3.
4. 512
5. 216
6. m5n3p3
 
 
 
2
6 31
2
x y

WHY is it helpful to write numbers in
different ways?
The Number System

Course 3, Lesson 1-3 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 8.EE.1
Know and apply the properties of integer exponents to generate
equivalent numerical expressions.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.

• To multiply and divide powers
The Number System

• monomial
The Number System

The Number System
Words To multiply powers with the same base, add their
exponents.
Numbers Algebra
Examples or4 3 4 3
2 2 2 
 7
2 m n m n
a a a 


1
Need Another Example?
2
3
4
Step-by-Step Example
1. Simplify using the Laws of Exponents.
52 • 5
52 • 5 = 52 • 51 5 = 51
The common base is 5.= 52 + 1
= 53 or 125 Add the exponents.
Simplify.
Check 52 • 5 = (5 • 5) • 5
= 5 • 5 • 5
= 53

Answer
Simplify 76 • 7 using the Laws of Exponents.
77

1
2
c3 • c5
c3 • c5 = c3 + 5 The common base is c.
Add the exponents.= c8

Answer
Simplify r4 • r6 using the Laws of Exponents.
r10

1
2
3
–3x2 • 4x5
–3x2 • 4x5 = (–3 • 4)( x2 • x5) Commutative and Associative Properties
The common base is x.= (–12)(x2 + 5)
= –12x7 Add the exponents.

Answer
Simplify −7x2 • 11x4 using the Laws of
Exponents.
−77x6

The Number System
Words To divide powers with the same base, subtract their
exponents.
Numbers Algebra
Examples
or
7
7 3
3
3
3
3

 4
3 , where 0
m
m n
n
a
a a
a

 

1
2
= 48 – 2 The common base is 4.
Simplify.= 46 or 4,096

Answer
Simplify using the Laws of Exponents.
610

1
2
= n9 – 4 The common base is n.
Simplify.= n5

Answer
Simplify using the Laws of Exponents.
a6

1
2
3
4
= Group by common base.
Subtract the exponents.= 23 • 31 • 51
23 = 8= 8 • 3 • 5
Simplify.= 120

Answer
Simplify .
450

1
2
3
7. Hawaii’s total shoreline is about 210 miles long.
New Hampshire’s shoreline is about 27 miles long.
About how many times longer is Hawaii’s shoreline
than New Hampshire’s?
To find how many times longer, divide 210 by 27.
Quotient of Powers= 210 – 7 or 23
Hawaii’s shoreline is about 23 or 8 times longer.

Answer
One centimeter is equal to 10 millimeters, and
one kilometer is equal to 106 millimeters. How
many centimeters are in one kilometer?
105 cm

How did what you learned
today help you answer the
different ways?
The Number System

How did what you learned
today help you answer the
different ways?
The Number System
Sample answer:
• If you need to multiply or divide large numbers that can
be written with the same base(s), it is easier to do when
the numbers are written in exponential form.

Explain how to
evaluate exponents
when multiplying and
dividing numbers with
the same base in
exponential form.
Ratios and Proportional RelationshipsThe Number System

Lesson 1.3 (8)

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Lesson 1.3 (8)