7.2 Properties of Rational Exponents

Review: Properties of ExponentsSame properties from Chapter 6

also apply to rational exponents.Product of Powers

Power of a Power

Power of a Product

Negative Exponents

Quotient of Powers

Power of a Quotient

Using the PropertiesSimplify each expression (no

negative exponents!)

Your Turn!Simplify:

Properties of RadicalsIf then the product and quotient

properties of exponents can be written using radical notation.

Using Properties of RadicalsSimplify each expression.

Your Turn!Simplify.

Writing Radicals in Simplest Form

Your Turn!Write in simplest form.

Adding and Subtracting RadicalsTwo radical expressions are like

radicals is they have the same index and radicand.

For example, and are like radicals.To add or subtract, use the

distributive property. Examples:

Your Turn!Perform the indicated operation.

Simplifying Expressions with VariablesValues of variables can be positive,

negative, or zeroSometimes absolute value is needed

when simplifying.

For now, we will assume all variables are positive.

To simplify:Apply properties of exponents

and/or radicals.Answer should have:

◦No negative exponents.◦Reduced coefficients.Example:

Examples:Simplify each expression.

Your Turn!Simplify each expression. Assume

all variables are positive.

Writing in Simplest FormJust like with numbers: Factor out perfect nth powers, rationalize denominators, and simplify.All powers left under the radical must be smaller than the index.Examples:

Your Turn!Write in simplest form. Assume all

variables are positive.

Adding and Subtracting Expressions with VariablesJust like with numbers, use the

distributive property to combine “like radicals.”

Examples:

Your Turn!Simplify each expression. Assume

all variables are positive.