Algebra 1 Common Core Student Edition, Grade 8-9

Thin k

Why must like

variables be grouped

together?

To s i m p l i f y b y a d d i n g

exponent s, t he bases

must be the same.

Pr o b lem 6 Si m p l i f y i n g Ex p r e ssi o n s W i t h Ra t i o n a l Ex p o n e n t s

Simplify the expression (2d • 3b* j ^ cC' • 5 b*).

= (2 • 3 • 5)( a? •. ^2 j Co m m u t at i ve an d asso ci at i v e p r o p er t i es o f m u l t i p l i cat i o n

= 3o(ai •. bkj Simplify.

= 30^ aij|h?J Add exponents that have the same base.

3

= 30 ab* Simplify.

Go t It? 6. Simplify each expression.

„ 3 1

a. 2 cs • 2 c=

c. • c^ j

b. m m

d. 13i/ i • 7m*) (376 • Trn^j

Do

1.

2.

3.

Lesso n Ch eck

you know HOW?

What is 84 • 88 written using each base only once?

2 3

What is the simplified form of 2m • 3ml

What is (3 X 105)(8 X 104) written in

scientific notation?

4. Measurement The diameter of a penny is about
   1.9 X 10 “5 km. It would take about 2.1 X 109 pennies
   placed end to end to circle the equator once. What is
   the approximate length of the equator?

_.............. MATHEMAtlCAL

Do yo u UN DERSTAN D? PRA CTI CES

5. Writ ing Can x 8 • y 3 be written as a single power?
   Explain your reasoning.


6. Reaso n i n g Suppose a X 10m and b X 10" are two
   numbers in scientific notation. Is their product
   ab X 10m+" always, sometimes, or never a number in
   scientific notation? Justify your answer.


7. Error Analysis Your friend says 4cb • 3m = let.
   Explain your friend's error. What is the correct answer?

Pr act i ce an d Pr o b l em - So l v i n g Ex er ci ses

Pr act i ce Rewrite each expression using each base only once.

MAIHEMAIICAL

PRA CTI CES

8. 7 3 • 7 4

11. 22 • 27 • 2 °

Simplify each expression.

14. m 3 m 4


15. (x 5 y 2 )(x- 6 y)
    9. ( -6)12 • (—6)5 • (—6)2


16. 5-2 • 5- 4 • 58


17. 5c4 • c 6


18. (5x5)(3y6)(3 x2)

Write each answer in scientific notation.

20. Biology A human body contains about 2.7 X 104 microliters (//.L) of blood for each
    pound of body weight. Each microliter of blood contains about 7 X 104 white blood
    cells. About how many white blood cells are in the body of a 140-lb person?

Se e Pr o b l e m 1.

10. 9 6 • 9-4 • 9~2


11. ( —8)5 • (—8)“5
    Se e Pr o b l e m 2.


12. 4 r 5 • 2 r 3


13. -m 2 • 4r 3 • 12r-4 • 5m
    4 ^ See Problem 3.

G

Po w erAlg eb ra.com Lesso n 7-2 Multiplying Powers With the Same Base^429