Assignment: 4.2: nth Roots and Rational Exponents

ALGEBRAIC REASONING - Spring 2026
2026-03-21T00:19:20Z

Due:

The goals of this lesson are that by the end of the lesson, you will be able to:

1. Convert between radicals and exponential notation

2. Evaluate Expressions with rational exponents

3. Apply the properties of exponents (you reviewed in the last lesson) to rational exponents

This is a big lesson, so we are going to break it down into smaller pieces. Feel free to take one piece at a time.

Let's get started!

1. Convert between radicals and exponential notation

Video 1: Introduction to Rational exponents

Now click the link for a quick practice of converting between radical and exponential notation: Practice problems 1

Video 2: More converting between radical and exponential notation

Now practice a few problems: Practice 2

And a few more: Practice 3

Great! You are on your way!

2. Evaluate Expressions with rational exponents

Video: Evaluating Expressions with Rational Exponents 1

Video: Evaluating Expressions with Rational Exponents 2

Now watch this video for a few practice problems, pause it to try the problems on your own, then play it again to check your answers: Practice examples video

3. Apply the properties of exponents to rational exponents

Use the handout linked here to explore using the properties of exponents with rational exponents. Do explorations #1-3, and "Communicate Your Answer."

Since you don't have a partner to talk to about these things, you can compare your answers with mine: Handout teacher answers

The main idea is that since we can change radicals into exponential notation, we can use all the properties of exponents on these re-written expressions!

That is what we are going to practice now - using all the properties of exponents on expressions with rational (fractional) exponents

Video: Using Product of Powers with rational exponents

Video: Using Power of a Power rule with rational exponents

A few problems to practice, with worked out solutions: Practice Problems 4

Nice job!

Now try the assignment on Wamap!

WaMap Assignment 4.2: nth Roots and Rational Exponents

The goals of this lesson are that by the end of the lesson, you will be able to:

1. Convert between radicals and exponential notation

2. Evaluate Expressions with rational exponents

3. Apply the properties of exponents (you reviewed in the last lesson) to rational exponents

This is a big lesson, so we are going to break it down into smaller pieces. Feel free to take one piece at a time.

Let's get started!

1. Convert between radicals and exponential notation

Video 1: Introduction to Rational exponents

Now click the link for a quick practice of converting between radical and exponential notation: Practice problems 1

Video 2: More converting between radical and exponential notation

Now practice a few problems: Practice 2

And a few more: Practice 3

Great! You are on your way!

2. Evaluate Expressions with rational exponents

Video: Evaluating Expressions with Rational Exponents 1

Video: Evaluating Expressions with Rational Exponents 2

Now watch this video for a few practice problems, pause it to try the problems on your own, then play it again to check your answers: Practice examples video

3. Apply the properties of exponents to rational exponents

Use the handout linked here to explore using the properties of exponents with rational exponents. Do explorations #1-3, and "Communicate Your Answer."

Since you don't have a partner to talk to about these things, you can compare your answers with mine: Handout teacher answers

The main idea is that since we can change radicals into exponential notation, we can use all the properties of exponents on these re-written expressions!

That is what we are going to practice now - using all the properties of exponents on expressions with rational (fractional) exponents

Video: Using Product of Powers with rational exponents

Video: Using Power of a Power rule with rational exponents

A few problems to practice, with worked out solutions: Practice Problems 4

Nice job!

Now try the assignment on Wamap!

WaMap Assignment 4.2: nth Roots and Rational Exponents