Unit 2: Rational Exponents and Radical Functions (BI Chapter 5): Properties of Rational Exponents and Radicals

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

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
You will be able to use the Properties of Radicals to simplify radical expressions

You will be able to Simplify Variable Expressions

Quick check: Identify the index and radicand of each and convert to the "other" form (radical to rational exponent or rational exponent to radical); then simplify:

$LaTeX: \sqrt[3]{9}\cdot\sqrt[3]{3}\cdot\sqrt[3]{125}$
$LaTeX: \sqrt[5]{4a^8b^{14}c^{50}}$
$LaTeX: \sqrt[4]{10}+7\sqrt[4]{10}$

Focus for today: combining LIKE Radicals!

Key understanding: two radicals are "like" if their index and radicand are identical. The radicals in part "C" of the warm up above are "alike" because they both have an index of 4 and a radicand of 10. If two radicals are alike you can combine them by adding (or subtracting) their coefficients. The coefficient of the first radical is 1 and the coefficient of the second is 7. So, to combine them, you know you have 8 of them. The result is $LaTeX: 8\sqrt[4]{10}$ .

If you are absent check out the unit resources linked below under the topic "Exponent Rules with Rational Exponents." Additionally, here are some documents you might find useful:

Homework HW 2.8: BI p. 248-249 #37-48 all; and 57-64 all. (Remember to try to make things smaller before you make them bigger -- try doing prime factorization of numbers, for example, to see what the nth roots might be).

Prep for mid-unit quiz-zesty TOMORROW!

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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Rational Exponents and Radical Functions Unit Resources Module

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)