1. Rational Exponents
What you’ll learn
To simplify expressions with rational exponents.
To convert rational exponents and radical forms
of expressions
Vocabulary
Rational exponent

2. Take a note:
You can write a radical expression in an equivalent
form using a fractional (rational ) exponent instead
of the radical sign. By definition
For any positive integer n. Like the radical form,
the exponent form indicates the principal root
Rational Exponent:

3. What is the simplify form of each expression?
Problem 1:Simplifying Expressions with Rational Exponents.
What is the simplify form of each expression?
Rewrite as radicals
Rewrite as radicals
Rewrite as radicals
Your turn:
Answers:
8,11,6

4. Take a note

5. Problem 2: Converting Between Exponential and
Radical Form
Answers

6. Your turn
Answers:

7. Sun-Mercury-Venus-Earth-Mars
Your turn again: Using Rational Exponents
Kepler’s Third Law of Orbital Motions shows how can approximate the period P(in Earth years) it takes a planet to complete one orbit of the sun. Use the function ,where d is the distance from the planet to the sun in astronomical units (AU is about 93,000,000 miles or the distance from Earth to the sun)
a)How many Earth years does it
takes to Mars to orbit the Sun?
Find approximate length in earth
years of each planet.
b)A Venusians year if Venus is 0.72 AU from the sun.
c) A Jovian year if Jupiter is 5.46 AU from the sun
1.52 AU
Sun-Mercury-Venus-Earth-Mars
Answers

8. Problem 3: Combining Radical Expressions
Answer
Your turn:
What is each product or quotient in simplest form
Answers

9. Problem 4: Writing expressions in the simplest form
What is each number or expression in the simplest form?

10. Your turn
What is each number or expression in the simplest form?
Answers

11. Classwork odd Homework even
TB pgs Exercises 10-90