Algebra 1 Common Core Student Edition, Grade 8-9

Sh o u l d y o u a d d
or multiply the
exponent s t o sim p lif y
the expression?
Yo u m u l t i p l y t h e
exponents when raising a
power to a power.

Sim p lif yin g a Po w er Raised t o a Po w er

0 What is the simplified form of (n4)7?

(n 4)7 = n4’7 Multiply exponents when raising a power to a power.

= « “8 Simplify.

0 What is the simplified form of (xi)^?

(xl)! = x H Multiply exponents when raising a rational power to a rational power.

2 1

= xe = x3 Simplify.

Go t It? 1. What is the simplified form of each expression in parts (a)-(d)?

a. (p5)4 b. (p4)5 c. (pty d. (p?)

e. Reasoning Is (a m)n = (an)m true for all integers m and n? Explain.

iu|2

Use the order of operations when you simplify an exponential expression.

Sim p lif yin g an Exp ressio n W it h Po w er s

What is the simplified form of y 3 (yi)~2?

What is t h e f i r st st ep

in si m p li f yin g t he

expression?

By t h e o r d er o f

operations, you simplify

powers before you

mult iply.

Th i n k

You multiply exponents when

raising a power to a power.

You add exponents when

multiplying powers with the

same base.

Writ e t he expression using

only positive exponents.

y (y2) = y y3vf-(-2)

o _10

=yy 2

,3+(-5)

= y-2

<9 Got It? 2. What is the simplified form of each expression?

a. x 2 (x6) - 4 b. C. (s 5) 2 ( 52 )

You can use repeated multiplication to simplify an expression like (4/722).

r(4 m 2 j° = 4m 2 • IxQ I I I4iw • 4nv

= 4 • 4 • 4 • mIII 2 • m 2 • m 2

o 3

= 4°mi

= 64/722^3

Notice that ( 4 /7^)3 = 43m i This example illustrates another property of exponents.

434 Ch a p t er 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