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4.1 Use Properties of ExponentsProperties of ExponentsLet a and b be real numbers and let m and n be integers.
Product of Powers Property ______aaa nm nm
Power of a Powers Property ______aanm mn
Power of a Product Property ______baab m m m
Negative Exponents Property 0 ,______ aa mma
1
Zero Exponent Property 0 __,0 aa 1
Quotient of Powers Property 0 ,______ aaa
an
mnm
Power of a Quotient Property 0 ,_________
ab
am
m
m
b
a
4.1 Use Properties of Exponents
Example 1 Evaluate a numerical expressionEvaluate a numerical expression
326 a. ____6 32 __6 6 ______ 656,46
3
5
4
4 b. ____4 35 __4 2 ___16
47 c.
_________
47
1_________
2401
1
4.1 Use Properties of ExponentsCheckpoint. Evaluate or simplify the expression.Checkpoint. Evaluate or simplify the expression.
1
2
5
8
8 1.
58
58
2838
1
512
1
28
4.1 Use Properties of Exponents
Example 2 Use scientific notation in real lifeUse scientific notation in real lifeIceland covers about 1.03 X 105 square kilometers and has a population of approximately 2.94 X 105 people. About how many people are there per square kilometer?Solution
_______________________________area Land
Population
51094.2 51003.1
Divide population by land area.
Quotient of powers property
_______________________________
03.1
94.2 010
Use a calculator__________ 85.2 010Zero exponent property_____ 85.2
There are about ___ people per square kilometer.3
4.1 Use Properties of Exponents
Example 3 Simplify expressionsSimplify expressions
815
325
a.yx
yx815
yx Power of a product
property 35x 32y
815
yx Power of a power
property
15x6y
_______Quotient of powers property
1515x 86y
_____ Simplify exponents0x 2y
_____ Zero exponent property2y
___________
Negative exponent property2
1
y
4.1 Use Properties of Exponents
Example 3 Simplify expressionsSimplify expressions2
2
4
b.
b
a
Power of a quotient property
24a
22b
Power of a power
property
8a4b
Negative exponent property
148ba
4.1 Use Properties of ExponentsCheckpoint. Simplify or evaluate the expression. Tell Checkpoint. Simplify or evaluate the expression. Tell which properties of exponents you used.which properties of exponents you used.
23 107104 2.
74 110Product of powers property
11028280
2108.2
4.1 Use Properties of ExponentsCheckpoint. Simplify or evaluate the expression. Tell Checkpoint. Simplify or evaluate the expression. Tell which properties of exponents you used.which properties of exponents you used.
3
5
22 3.
ba
ba
Power of a quotient/product property 2 3
32a 3b
35a 3b Power of a power property
8
6a 3b15a 3b
Quotient of powers property
8
9a
4.1 Use Properties of Exponents
Example 4 Compare real-life volumesCompare real-life volumesBeach Ball The radius of a beach ball is about 5.6 times greater than the radius of a baseball. How many times as great as the baseball’s volume is the beach ball’s volume?Let r represent the radius of the baseball
3
3
34
34
volumesBaseball'
volumesball'Beach
r
r6.5 The volume of a sphere is
Power of a Product property property
3 34
34
r
336.5 r
. 3
4 3r
4.1 Use Properties of Exponents
Example 4 Compare real-life volumesCompare real-life volumesBeach Ball The radius of a beach ball is about 5.6 times greater than the radius of a baseball. How many times as great as the baseball’s volume is the beach ball’s volume?Let r represent the radius of the baseball
_______ 036.5 r Quotient of Powers
Zero Exponent Property____ 36.5Approximate power____176
The beach ball’s volume is about ____ times as great as the baseball’s volume.
176
4.1 Use Properties of ExponentsCheckpoint. Complete the following exercise.Checkpoint. Complete the following exercise.4. Rework Example 4 where the radius of a
beach ball is about 6 times the radius of a baseball.
3
3
34
34
r
r63
336
r
r 36 216
216 times as great
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