Algebra 1 Common Core Student Edition, Grade 8-9

When can you use
the property for
multiplying powers?
Yo u c a n u se t h e p r o p e r t y
for multiplying powers
when the bases of the
powers are the same.

3

Pro b lem 1 Multiplying Powers

What is each expression written using each base only once?

Q 124 • 123 = 124+3 Add the exponents of the powers wit h the same base.

= 127 Simplify the exponent.

0 ( 5) 2( 5)7 = (—5) _2+7

= (-5)5

Add the exponents of the powers wit h the same base.

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

Got It? 1. What is each expression written using each base only once?

a. 83 • 86 b. (0.5)~ 3 (0.5)-8 C. 9 -3 • 9 2 •

When variable factors have more than one base, be careful to combine only those

powers with the same base.

Plan

Which parts of the

exp ression can you

com bine?

Yo u c a n g r o u p t h e

coefficients and multiply.

Yo u c a n a l so w r i t e a n y

powers that have the

same base wi t h a si ngl e

exponent.

Pro b lem 2 M u lt ip lyin g Po w er s in A lg eb r aic Exp ressio n s

What is the simplified form of each expression?

0 4z 5 • 9z 12 = (4 • 9)(z’ • z 12)

= 36(z5+(~12))

= 36z~

= M_7

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

Multiply the coefficients. Add the exponents of the powers

with the same base.

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

Rew r i t e u si n g a p o si t i v e exp o n en t.

02a • 9b 4 • 3a 2 = (2 • 9 • 3)(a • a‘

= 54 (a* a 2 )(b4)

= 54(a 1 + 2 )(b4)

t 1

*1+2

= 54a 3 b 4

Commutative and associative properties

of multiplication

Multiply the coefficients. Write a as a1.

Add exp onent s of powers wit h t he same base.

Si m p l i f y.

v# Got It? 2. What is the simplified form of each expression in parts (a)-(c)?

a. 5x 4 • x 9 • 3x b. -4c 3 • 7 d 2 • 2c~2 c. j2 • k~2 • 12j

d. Reasoning Explain how to simplify the expression xa • xb • xc.

426 Ch ap t e r 7 Ex p o n e n t s a n d Ex p o n e n t i a l Fu n c t i o n s