Algebra 1 Common Core Student Edition, Grade 8-9

Plan
In radical f orm, do you
use the numerator or
denominat or as t he
index?
You use the denominator
of the rational exponent
as the index of the
radical.

Can y o u w r i t e

^27d5 as 27c/ l?

No. Since the coefficient

27 is under t he radical,

the index operates

on the coefficient as well

as t he var i ab l e.

Go t It? 1. What is the simplified form of each expression?

a. iff? b. V32 C. i/ff d. if 36

o

You can also write expressions that have rational exponents like ~ in radical form.

83 = 82'5 = (82)3 =

85 = 85'2 = (83 )2 = (V8)2

So, 8 * = = ( i/ 8 ) 2.

Key Concept Equivalence of Radicals and Rational Exponents

If the nth root of a is a real number and m and n are positive integers, then

1

an5 = ifa and a * =.

Co n v e r t i n g t o Rad i cal Fo r m

o What is 12m in radical form?

12ol = 12ifcf Re w r i t e as in radical form.

O What is (64a)s in radical form?

4 4

(64a)s = (32 • 2 Si n c e 3 2 i s t h e 5 t h p o w e r o f 2 , w r i t e 6 4 a a s a p r o d u c t o f 3 2 an d 2 a.

Po w er o f a p r o d u ct

Re w r i t e 32 as 2 5.

= 32s(2 of

= 251 • ( 2 n)l

= 24 • ( 2 a)l Si m p l i f y 5 • j.

= 16 V (2a)4 Simplify and write (2a)t in radical form.

^ Got It? 2. What is each exponential expression in radical form?

b. 5x3 c. (54y)

Pro b lem 3 J Co n v er t i n g t o Ex p o n en t i al Fo r m

Q What is 'fb3 in exponential form?

iflf = h i Rewrite using exponential form.

Q What is v27 d5 in exponential form? Simplify.

i/27d5 = (27d5)3 Rewrite the radical expression in exponential form.

= 275(d5)s Power of a product

=^3 di Simplify.

c

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