Rational Exponents and reducing radicals Unit 3 Day 1

Warm Up Quincy has been confused about simplifying algebraic expressions. His brother Oscar prepared this quiz for him to practice. Look at Quincy’s responses below. If the response is correct, write correct. If it is incorrect, write the correct answer.

4𝑦 – 5𝑦 −𝑦 3𝑥+2𝑥 5 𝑥 2 2 𝑛 2 +4 𝑛 2 6 𝑛 4 2𝑥∗3𝑦 5𝑥𝑦 2𝑎−(𝑎−𝑏) 𝑎−𝑏 Correct 5𝑥 6 𝑛 2 6𝑥𝑦 𝑎+𝑏

1+ 5 𝑛 𝑛+5 𝑛 5 4−(𝑛+7) −3−𝑛 2 𝑥 6 𝑥 3 2 𝑥 2 2𝑥𝑦 2 4 𝑥 2 𝑦 2 2𝑎+3𝑏+3𝑎+4𝑏 6 𝑎 2 +12 𝑏 2 Correct 2 𝑥 3 Correct 5𝑎+7𝑏

Notes Using your calculator, complete the following table.

Expression Numerical Value (4) 1 2 =? (64) 1 3 =? 2 4 1 = 4 =? 3 64 1 =? (8) 2 3 =? 3 8 2 =? (16) 1 4 =? (25) −1 2 =? 4 16 1 =? 2 25 −1 = 1 25 =? ( 2 3 ) 1 2 =? 2 (2) 3 =?

What did you notice about your answers to the problems in the same rows?

Is there some pattern that relates the two expressions in each row to one another? Describe the pattern.

Interactive Notebook 𝑥 = 𝑥

Given the expression 5 3 1/4 , what expression using a root symbol would yield the same numerical value?

Given the expression 3 54 , what expression utilizing a fractional exponent would yield the same numerical value?