Properties of Rational Exponents Section 7.2

WHAT YOU WILL LEARN: 1. Simplify expressions with rational exponents. 2. Use properties of rational exponents. 3. Write an expression involving rational exponents in simplest form. 4. Perform operations with rational exponents. 5. Simplify expressions that have variables and rational exponents. 6. Write an expression involving variables and rational exponents in simplest form. 7. Perform operations with rational exponents and variables.

Properties of Rational Exponents Properties of Rational Exponents: Property:Example: (a m ) n = a mn 3. (ab) m = a m b m 4.

Properties of Rational Exponents (cont.) Properties of Rational Exponents: Property:Example: 5. 6.

Using the Properties Simplify the expressions:

More Fun with Properties 4. 5.

You Try Simplify:

More Simplifying Simplify the expressions: 1. 2.

You Try Simplify: 1. 2.

Simplest Form - continued In order for a radical to be in simplest form, you have to remove any perfect n th powers and rationalize denominators. Example: Write in simplest form: 1.2.

You Try Write in simplest form: 1. 2.

Operations Using Radicals Two radicals expressions are “ like radicals ” if they have the same index and the same radicand. Example: Perform the indicated operation: 1.2.

You Try Perform the indicated operation: 1. 2.

Simplifying Expressions Involving Variables Important! = x when n is odd. = |x| when n is even.

Simplifying Simplify the expression. Assume all variables are positive:

You Try Simplify the expression. Assume all variables are positive

Writing Variable Expressions in Simplest Form Write the expression in simplest form. Assume all variables are positive. 1.2.

You Try Write the expression in simplest form. Assume all variables are positive

Adding and Subtracting Expressions Involving Variables Perform the indicated operation. Assume all variables are positive

You Try Perform the indicated operations. Assume all variables are positive

Homework page 411, even, even, even, 76, 80 :