Download 3 - Algebra 1

Lesson 7-5 Warm-Up
ALGEBRA 1
“Division Properties of Exponents”
(7-5)
How do you
divide powers
with the same
base?
Rule: When you divide numbers with the same base, subtract the
exponents.
m
m-n
a =a
bn
1
1
4
Example: a = a · a · a · a = a2
a2 = a · a
1
1
ALGEBRA 1
Division Properties of Exponents
LESSON 7-5
Additional Examples
Simplify each expression.
a.
Subtract exponents when dividing
powers with the same base.
x4
4–9
x
=
9
x
= x–5
Simplify the exponents.
1
Rewrite using positive exponents.
= x5
b.
p3 j –4
p3 – (–3)j
=
–3
6
p j
= p6 j –10
p6
= j10
–4 – 6
Subtract exponents when dividing
powers with the same base.
Simplify.
Rewrite using positive exponents.
ALGEBRA 1
“Division Properties of Exponents”
(7-5)
How do you
divide numbers
in scientific
notation form?
Rule: When you divide numbers in scientific notation, divide the decimals
and the exponents separately.
Example:
To find average, divide the number of tons by
number of people
ALGEBRA 1
Division Properties of Exponents
LESSON 7-5
Additional Examples
A small dog’s heart beats about 64 million beats in a
year. If there are about 530 thousand minutes in a year, what is
its average heart rate in beats per minute?
6.4  107 beats
64 million beats
=
530 thousand min
5.3  105 min
6.4
 107–5
Subtract exponents when dividing
powers with the same base.
6.4
5.3
 102
Simplify the exponent.
= 5.3
=
Write in scientific notation.
1.21  102
Divide. Round to the nearest hundredth.
121
Write in standard notation.
The dog’s average heart rate is about 121 beats per minute.
ALGEBRA 1
““Division Properties of Exponents”
(7-5)
What happens
when you raise a
quotient (like a /
b) to a power?
Rule: When you raise a quotient to a power [Example: (a / b)m, where a and
b are nonzero numbers], raise the dividend and divisor (a and b) to the
power separately.
ALGEBRA 1
Division Properties of Exponents
LESSON 7-5
Additional Examples
3 4
Simplify y 3 .
3
y3
4
34
= 34
(y )
Raise the numerator and the
denominator to the fourth power.
34
= y 12
Multiply the exponent in the denominator.
81
= y 12
Simplify.
ALGEBRA 1
Division Properties of Exponents
LESSON 7-5
Additional Examples
a. Simplify
2
3
–3
=
–3
2
3
3
2
.
3
2
Rewrite using the reciprocal of 3 .
Raise the numerator and the
denominator to the third power.
33
= 23
27
3
= 8 or 3 8
Simplify.
ALGEBRA 1
Division Properties of Exponents
LESSON 7-5
Additional Examples
(continued)
–2
4b
b. Simplify – c
– 4b
c
–2
.
=
– c
4b
2
=
-c
4b
2
Rewrite using the reciprocal of – 4b .
c
Write the fraction with a negative numerator.
(–c)2
= (4b)2
Raise the numerator and denominator
to the second power.
c2
= 16b2
Simplify.
ALGEBRA 1
Division Properties of Exponents
LESSON 7-5
Lesson Quiz
Simplify each expression.
1.
a8
a–2
4.
1.6  103
4  10–2
a10
2.
4  104
5.
w3
w7
24
5
1
w4
2
6
10
25
4
–2
3. (3a) (2a )
6a2
6.
4x 3
3x 2
27
–3
27
64x3
ALGEBRA 1