Upload
wesley-dennis
View
214
Download
0
Embed Size (px)
Citation preview
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.
Example: = a2
am = am - n
bn
ALGEBRA 1
Simplify each expression.
x4
x9a.
Simplify the exponents.= x–5
Rewrite using positive exponents. 1 x5=
p3 j –4
p–3 j 6
= p6 j –10 Simplify.
Rewrite using positive exponents.p6
j10=
b.
=Subtract exponents when dividing powers with the same base.
x4 – 9
=Subtract exponents when dividing powers with the same base.
p3 – (–3)j –4 – 6
Division Properties of ExponentsLESSON 7-5
Additional Examples
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
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?
64 million beats 530 thousand min
6.4 107 beats
5.3 105 min= Write in scientific notation.
6.45.3 107–5=
Subtract exponents when dividing powers with the same base.
6.45.3 102= Simplify the exponent.
The dog’s average heart rate is about 121 beats per minute.
Division Properties of ExponentsLESSON 7-5
Additional Examples
121 Write in standard notation.
1.21 102 Divide. Round to the nearest hundredth.
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
Simplify . 3 y 3
4
34
y 12= Multiply the exponent in the denominator.
81y 12= Simplify.
3 y 3
4 34
(y 3)4=
Raise the numerator and the denominator to the fourth power.
Division Properties of ExponentsLESSON 7-5
Additional Examples
ALGEBRA 1
a. Simplify .23
–3
33
23=Raise the numerator and the denominator to the third power.
Simplify.278 3
38or=
23
–3 32
3= Rewrite using the reciprocal of .
23
Division Properties of ExponentsLESSON 7-5
Additional Examples
ALGEBRA 1
(continued)
b. Simplify
Raise the numerator and denominator to the second power.
(–c)2
(4b)2=
Simplify.c2
16b2=
4bc
–
4bc
––2 c
4b–
2= Rewrite using the reciprocal of .4b
c–
Write the fraction with a negative numerator.- c 4b
2=
–2
.
Division Properties of ExponentsLESSON 7-5
Additional Examples
ALGEBRA 1
Simplify each expression.
1. 2. 3.
4. 5. 6.
a8
a–2
w3
w7
(3a)4(2a–2)6a2
1.6 103
4 10–2
24
54x 3
3x 2
a10 1 w4 27
4 104 10 6 25
27 64x3
2 –3
Division Properties of ExponentsLESSON 7-5
Lesson Quiz