UNIT 7 : POWER, ROOTS, AND EXPONENTS
MA40: ALGEBRA II
7.1 – nth Roots and Rational Exponents
(Text Ref: Ch 7.1, Pg 401-406)
Standards: MA40-S1C1-02, MA40-S3C3-02, 05
Objective: TSWD synthesis of rational exponents by discovering the relationship between nth roots and
exponents and then make inferences regarding the properties of rational exponents.
Definition of
nth Root of an
Expression
I. nth Root of an Expression
A. Definition of the “nth Root of a ”
index
radical
radicand
Example:
Evaluate 3 27  ?
Question: “What number, when you raise it to the 3rd power
gives you 27?“
3
Since 3  27 we know 3 27  3
B. Simplify the Radical Expression
a)
5
64
b)
d)
4
243a 4
e)
4
81x 4 y
c) 33 54 x 5
72x 3
f) 53 80n 5 m 3
Simplify the
Radical Expression
Rational Exponents
Definition (part 1)
II. Rational Exponents
A. Definition of Rational Exponents (part 1)
For any real number b and for any positive integer n,
Rewrite
Radical  Rational
Notation
B. Rewrite the expression using rational exponent notation.
a) 3 11
b) 4 x
c) 5 2a
Rewrite
Rational  Radical
Notation
C. Rewrite the expression using radical notation
a) 51 2
b) a 1 4
c) 3xy
13
7.1 – nth Roots and Rational Exponents (continued)
Definition (part 2)
D. Definition of Rational Exponents (part 2)
For any nonzero real number b and for any positive integer m
and n, with n  1,
E. Rewrite the expression using rational exponent notation.
Rewrite
Radical  Rational
Notation
Rewrite
Rational  Radical
Notation
a)
4
53
b)
 3x 
5
2
c)
F. Rewrite the expression using radical notation
34
a) 8 2 3
b) 5b 
6
2x 3
c) 79 xy
III. Evaluate Rational Expressions
A. Evaluate the Expression with Rational Exponents
Evaluating
Rational Expressions
3
a) 243 5
Method 1
Method 2
B. Evaluate the Rational Expressions
a) 9 3 2
b) 16 5 2
d) 64 5 2
e) 64 2 3
c) 32 2 5
27