Algebra 1 Common Core Student Edition, Grade 8-9

How do you find the
ar ea of t he sq uar e?
Th e ar ea o f a sq u ar e
with side length s is s 2.
Sq u ar e t h e si d e l en g t h
of the square to find the
area.

What is the exponent
of m?
It has an implied
exponent of 1. Similar to
coefficient s, exponent s
of 1 don't need to be
written.

Pro p ert y Raising a Product to a Power

Words To raise a product to a power, raise each factor to the power and multiply.

Algebra (ab)n = anbn, where a 0 , b # 0 , and n is a rational number

Ex a m p l e s (3x)4 = 3 4 x 4 = 81x4 (4fo)t = ibi = 8 bi

Sim p lif yin g a Pro d u ct Raised t o a Po w er

Multiple Choice Which expression represents the area of the square?

<3D 10 x 3 CCD 25x5

GD 5x6 dD 25x6

(5x3)2 = 5 2 (x3)2 Rai se e ac h f a c t o r t o t h e sec o n d p o w er.

= 5 2 x 6 Multiply the exponents of a power raised to a power.

= 25x6 Si m p l i f y.

The correct answer is D.

sjG o t It? 3. What is the simplified form of each expression?

a. (7m9) 3 b. (2z)~4 c. (3g4)

5x3

4s-2

Si m p l i f y i n g a n Ex p r e ssi o n W i t h Pr o d u ct s

What is the simplified form of (n ^)10 ( 4 m n ^ )3?

(n 2 ) 10 ( 4 mn“i)3 = (m) 1043 m 3 (n-i)3 Rai se each f a c t o r o f 4 mn_3 to the third power.

= n543m3n~2 Multiply the exponents of a power raised to a power.

= 43m 3n 5n~2 Commutative Property of Multiplication

= 43m3n5+(~2^ Add the exponents of powers with the same base.

= 64m3«3 Si m p l i f y.

Go t It? 4. What is the simplified form of each expression?

a. (x~2)2(3xy5)4 b. (3cl)4(c2)3 c. (6ab)3{5a 3)2

You can use the property of raising a product to a power to solve problems involving

scientific notation. For example, to simplify the expression (3 X 108)2, you raise both

3 and 10 8 to the second power. Then multiply the two powers.

Lesso n 7- 3 M o r e M u l t i p l i cat i o n Pro p ert i es o f Exp o n en t s 435