Unit 2, Day 5: Rational Exponents and Radical Functions (BI Chapter 5, Section 2): Simplifying with Properties of Rational Exponents and Radicals

This section's Learning Objectives (we will be working on these for several days):

You will be able to convert expressions using rational exponents to radical expressions (and back)
You will be able to use the Properties of Integer Exponents to Rational Exponents to simplify radical expressions
- Simplifying Expressions with Rational Exponents
- Simplifying Products & Quotients of Radicals
You will be able to use the Properties of Radicals to simplify radical expressions
- Write radicals in simplest form
- Recognize and combine like radicals
- Add & subtract radicals and roots

You will be able to Simplify Variable Expressions
- Write variable expressions in simplest form
- Add & subtract variable expressions
You will continue building fluency with perfect squares (to 20), perfect cubes (to 10), powers of 2, powers of 3, and powers of 10

1) Warm Up Math Facts: Exponents and . . .

2) Applying Properties of Rational Exponents and Radicals: simplifying. Take notes in class, if you are absent, look at the unit resources linked below under the topic "Exponent Rules with Rational Exponents." Additionally, here are some documents you might find useful:

5.2 Simplifying Radical Expressions
5.2 Simplifying Radicals, Rationalizing the Denominator (note that some instructions don't apply!)
5.2 Student Journal covers all of the ideas for this section, including some we will be doing in the next couple of days.

Homework HW 2.5: BI p. 248 #1-20.

General Homework Expectations: Whether you are doing a homework assignment from the BI book, a worksheet, or some other activity, even a Desmos activity, please remember to write all the problems and show your processes in your composition (or note) book. Lists of answers without process will not receive credit!

As always, if you are struggling, be sure to check out the resources on this topic (linked below) . . . and if that's not enough, come by after school for support.

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Unit 2: Radical Functions and Rational Exponents Learning Resources

Numeracy facts you should master! These basics will help you make sense of what we're doing with exponents and radicals.

Squares to 20
Cubes to 10
Powers of 2, up to $LaTeX: 2^{10}=1,024$
Powers of 3, up to
Powers of 10 (Scientific Notation)