1. Simplify each expression.
Warm Up
Simplify each expression.
1. 73 • 72 2.
118
116
3. (32)3 4. 75 20 7 5.

2. Objectives Vocabulary
Rewrite radical expressions by using rational exponents.
Simplify and evaluate radical expressions and expressions containing rational exponents.
Vocabulary
index
rational exponent

3. The nth root of a real number a can be written as the radical expression , where n is the index (plural: indices) of the radical and a is the radicand. When a number has more than one root, the radical sign indicates only the principal, or positive, root.
When a radical sign shows no index, it represents a square root.
Reading Math

4. Example 1: Finding Real Roots
Find all real roots.
A. sixth roots of 64
B. cube roots of –216
C. fourth roots of –1024

5. The properties of square roots also apply to nth roots.
When an expression contains a radical in the denominator, you must rationalize the denominator. To do so, rewrite the expression so that the denominator contains no radicals.
Remember!

6. Example 2: Simplifying Radical Expressions
Simplify each expression. Assume that all variables are positive.

7. A rational exponent is an exponent that can be expressed as , where m and n are integers and n ≠ 0. Radical expressions can be written by using rational exponents. m n
The denominator of a rational exponent becomes the index of the radical.
Writing Math

8. Example 3: Writing Expressions in Radical Form
Write the expression (–32) in radical form and simplify. 3 5

9. Example 4: Writing Expressions by Using Rational Exponents
Write each expression by using rational exponents. A. B.

10. Rational exponents have the same properties as integer exponents

11. Example 5: Simplifying Expressions with Rational Exponents
Simplify each expression.

12. Example 6: Chemistry Application
Radium-226 is a form of radioactive element that decays over time. An initial sample of radium-226 has a mass of 500 mg. The mass of radium-226 remaining from the initial sample after t years is given by To the nearest milligram, how much radium-226 would be left after 800 years?
Pg , 85-88