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