Unit 4 PacketMPLG

1 1 College Prep Algebra 2 Unit 4: radical Expressions and Rational Exponents (Chapter 7) Name: _____ Teacher: _____ Period: _____ 2 Unit 4 radical Expressions and Rational Exponents (chapter 7) Learning Targets: Properties of Exponents 1. I can use properties of exponents to simplify expressions. Simplifying radical Expressions 2. I can simplify radical algebraic expressions. Multiplying and Dividing 3. I can multiply radical expressions. 4. I can divide radical expressions (and rationalize a denominator). Major Operations 5. I can add and subtract radical expressions. 6. I can multiply and rationalize binomial radical expressions.

2 Rational Exponents 7. I can convert from rational exponents to radical expressions (and vice versa). 8. I can simplify numbers with rational exponents. Solving radical Equations 9. I can solve equations with roots. 10. I can solve equations with rational exponents. Graphing Radicals 11. I can graph radical expressions & identify domain and range of radical expressions. Corresponding Book Sections LTs Book Section 1 7- 0 2 7- 1 3,4 7- 2 5,6 7- 3 7,8 7- 4 9,10 7- 5 11 7- 8 3 Properties of Exponents Date: _____ Quiz On: _____ After this lesson and practice, I will be able to.

3 Use properties of exponents to simplify (LT 1) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Before we learn about a new family of functions, it is important that we first pause to review the _____ properties you learned in Algebra 1. First, a review of the vocabulary: A useful method of remembering the exponent properties is through _____ _____.

4 If the exponent of a power is a positive integer, you can write it in expanded form. For example: Summary of exponent rules: Power Property of Equality: Common Base Property of Equality: Example 1: Simplify each expression completely. A) ()()3235 B) 25333 C) 36455 Example 2: Simplify 24213 4 You can use properties of exponents to simplify _____ expressions. A simplified expression contains only _____ exponents.

5 Example 3: Simplify each expression. Use only positive exponents in your solution. A) 586www B) 324rc C) 546162mnn D) ()34334xyxy Example 4: Simplify each expression. Use only positive exponents in your solution. A) ( 4x2)( 2x 2) B) 2w 3m4 5 C) 12m2n6()28m4n7 D) ()2534732xyxy FINAL CHECK: (calc allowed) LT 1. I can use properties of exponents to simplify expressions. 1. Simplify each expression.

6 Use only positive exponents in your solution. a. 5x6()2x 4y() 6x 3y4() b. ( 3x5y) 2 c. x4y 3()4x0y2 5 Practice Assignment (LT1) LT1. I can use properties of exponents to simplify expressions. o BOOK 7. 0 page 368 LT 1 MORE PRACTICE #1 (Yay!!!!) 1) 92 = 6) xy 5 = 2) 43x = 7) (xy)- 5 3) (- 4x)- 3 = 8) 24x 4) 72 = 9) (2x)- 4 5) 102 = 10) 2322 + 1) 181 4) 149 7) 155xy 9) 1164x 2) 43x 5) 1100 3) 1643x 6) xy5 8) 24x 10) 1336 6 LT 1 More Practice #2 Simplify.

7 Notice in these examples, some have negative exponents & some don t! a) 5x- 1 1) 2x- 5 b) 2- 5 2) 2- 3 c) (- 2)3 3) - 2x4 d) - 2x3 4) (- 2)4 = e) (- 2)- 3 5) (- 2)- 4 = f) 5x2y- 3 = 6) 7a5b- 10 = g) 5y3x- 2 7) - 10a2b- 3c- 4 h) 52ab- 3 8) (a5 b2)- 3 i) (5b3 )- 2 9) (4x5 )- 2 j) (- 2a2b4)3 10) (- 5x4 )- 3 k) (5x)- 2 y3 l) (7a)2 b- 3 m) 4x- 2yz- 1 n)

8 82061035245xyzxyz = LT 1 More Practice #3 11) (- 2) 2(- 2) 3 12) [- 32 ] 3 13) (32x2y)2 14) 5553 15) (2- 3) 2 16) mm741 17) 888359 18) 345 19) 3204xyz 7 20) 5836435354xyxxyy 21) 26412643235xyxxyy 22) xyzxyz 73214 23) 515310xyzyz 24) 03421003742952 zyxbcacbazyx 8 Simplifying radical Expressions Date: _____ Quiz On: _____ After this lesson and practice, I will be able to.

9 Simplify radical algebraic expressions. (LT 2) - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Warm Up: Write each number or expression as the square of a number or expression ( 16 = 42). a. !449 b. !!x10 c. !!144x6y8 Since 52 = 25, 5 is a square root of 25.

10 Since 54 = _____, 5 is a _____ root of _____. Since 53 = ____, 5 is a _____ root of _____. Since 55 = _____, 5 is a _____ root of _____. Definition: nth Root For real numbers a and b and any positive integer n, if _____ then _____ is an nth root of _____. Notation: What are the real fourth root(s) of 16? _____. What are the real fourth root(s) of - 16? _____. What are the real cube root(s) of - 8? _____. Type of Number Number of nth Roots when n is even Example Number of nth Roots when n is odd Example Positive 0 Negative Example 1: Find all real roots of each number.