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

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:

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

Take a note

Problem 2: Converting Between Exponential and Radical Form Answers

Your turn Answers:

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

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

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

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

Classwork odd Homework even TB pgs 386-387 Exercises 10-90