Download 6.4 Rational Exponents Name: Objective: To simplify expression

6.4 Rational Exponents
Objective: To simplify expression with rational exponents
Name:
Rational Exponent:
If the nth root of a is a real number, m is an integer and
m
is in lowest terms, then
n
If m is negative, a  0 .
Example 1: Simplifying Expressions with Rational Exponents
What is the simplified form of each expression?
1
1
1
B. 72  72
A. 216 3
1
Example 2: Converting Between Exponential and Radical Forms
3
A. What are x 7 and y 3.5 in radical form?
a5 and
B. What are
 b  in exponential form?
5
3
Try
A. What are w
B. What are
4

5
8
and w 0.2 in radical form?
x 3 and
 y  in exponential form?
5
4
Example 3: Using Rational Exponents
Planetary Motion: Kepler’s Third Law of Orbital Motion shows how you can
approximate the period P (in Earth years) it takes a planet to complete one
3
1
C. 54  125 4
orbit of the sun. Use the function P  d 2 , where d is the distance from the
planet to the sun in astronomical units (AU – about 93,000,000 miles or the
distance from the Earth to the sun). How many Earth years does it take Mars
to orbit the sun?
Example 4: Combining Radical Expressions
What is the simplest form of the expression?
4
A.
8
x3
x
B.
2
3
 3
4
x3
C.
3
x
D.
2
Example 5: Simplifying Numbers With Rational Exponents
What is each number in simplest form?
A. 162.5
Method 1
Method 2
Method 1
Method 2
4
B.  32  5
Simplest Form of an expression with rational exponents:
Example 6
What is each number in simplest form?

A. 8x
C.


1
15  3

8x xy
B. 9x y

2
3
Assignment: p.386 10-66 even, 86, 87

4
D. 16y 8

3
2


3
4
7
 7
3