Rational Numbers as Exponents Section 7-5. Objectives To calculate radical expressions in two ways. To write expressions with rational exponents as radical.

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Presentation transcript:

Rational Numbers as Exponents Section 7-5

Objectives To calculate radical expressions in two ways. To write expressions with rational exponents as radical expressions and vice versa. To simplify expressions containing negative rational exponents. To use rational exponents to simplify radical expressions.

Simplify and Compare

Theorem 7-6

We can raise to a power and then take a root or we can take a root and then raise to a power.

Definition

Write with rational exponents

What is Write as a radical Write with Rational Exponents

Negative Rational Exponents

Variables w/ Exponents Reminder: When Multiplying Expressions with similar Bases the Exponents ADD! When Dividing Expressions with similar Bases the Exponents SUBTRACT!

Variables w/ Exponents When Taking an Exponential of an Expression with a similar Base the Exponents MULTIPLY! Reminder: Negative Exponents mean you TAKE THE RECIPROCAL!

Using Rational Exponents to Simplify Radical Expressions Convert radical expressions to exponential expressions. Use the properties of exponents to simplify. Convert back to radical notation when appropriate.

Use Rational Exponents to Simplify

Write as a Single Radical Expression

Methods to Simplify Radical Expressions Simplify by factoring Rationalize denominators Collecting like radical terms Using rational exponents

Now you can Calculate radical expressions in two ways. Write expressions with rational exponents as radical expressions and vice versa. Simplify expressions containing negative rational exponents. Use rational exponents to simplify radical expressions.