Algebra 1 Common Core Student Edition, Grade 8-9

Think,—
How are the
properties for
dividing powers and
m ult ip lying p ow ers
si m i l ar?
Fo r b o t h p r o p e r t i e s , t h e
bases of the powers must
be t he same. Dividing
a power is the same as
multiplying by a negative
exponent.

Pro b lem 1 Dividing Algebraic Expressions

What is the simplified form of each expression?

□

X?

~x^ 5

X 2

=X 2

= JC 2

,m 2 n 4

Su b t r a c t e x p o n e n t s w h e n d i v i d i n g p o w e r s w i t h t h e sa m e b ase.

Si m p l i f y.

= m2~5n4~3

= m °nL

Su b t r a c t e x p o n e n t s w h e n d i v i d i n g p o w e r s w i t h t h e sa m e b ase.

Si m p l i f y t h e e xp o n e n t s.

Re w r i t e u si n g p o si t i v e e xp o n e n t s.

^ Got It? 1. What is the simplified form of each expression?

a. h *L

d3

6 ; 2

C.

kj 5

d.

-3b 7

a5b2

e.

sV^8

x4y~5z

You can use the property of dividing powers with the same base to divide numbers in

scientific notation.

Dividing Numbers in Scientific Notation

Demographics Population density describes the number of people per unit area.

During one year, the population of Angola was 1.21 x io 7 people. The area of Angola

is 4.81 x 105 m i2. What was the population density of Angola that year?

Know _ Need | t fflart ...... ...

• The population The population W rite the ratio of population to area.


• The area density

1-21 x 10 ' _ 1.21 x jq7 —5 S ubtract exponents w h e n dividing powers

4.81 x io ° 4 81 w jth the sam e base.

= X 102 Simplify the exponent.

= 0.252 X 10 2 Divide. Round to the nearest thousandth.

= 2 5. 2 W rite in standard n o ta tio n.

The population density of Angola was about 25.2 people per square mile.

Go f It? 2. During one year, Honduras had a population of 7.33 X 106 people. The

area of Honduras is 4.33 X 1^04 mi2. What was the population density of

Honduras that year?

440 Ch ap t er 7 Ex p o n en t s an d Ex p o n en t i al Fu n ct i o n s