1. Lesson 1 Menu Five-Minute Check (over Chapter 6) Main Ideas and Vocabulary Targeted TEKS Example 1: Identify Monomials Key Concept: Product of Powers Example 2: Product of Powers Key Concept: Power of a Power Example 3: Power of a Power Key Concept: Power of a Product Example 4: Power of a Product Concept Summary: Simplifying Expressions Example 5: Simplify Expressions

2. Lesson 1 MI/Vocab monomial constant Multiply monomials. Simplify expressions involving powers of monomials.

3. Lesson 1 Ex1 Identify Monomials Determine whether each expression is a monomial. Explain your reasoning.

4. A.A B.B C.C D.D Lesson 1 CYP1 Which expression is a monomial? A.x 5 B.3p – 1 C. D.

5. Key Concept 7-1a

6. Lesson 1 Ex2 Product of Powers A. Simplify (r 4 )(–12r 7 ). (r 4 )(–12r 7 ) = (1)(–12)(r 4 )(r 7 )Group the coefficients and the variables. = –12(r 4+7 )Product of Powers Answer: = –12r 11 Simplify.

7. Lesson 1 Ex2 Product of Powers B. Simplify (6cd 5 )(5c 5 d 2 ). Answer: = 30c 6 d 7 Simplify. (6cd 5 )(5c 5 d 2 )= (6)(5)(c ● c 5 )(d 5 d 2 )Group the coefficients and the variables. = 30(c 1+5 )(d 5+2 )Product of Powers

8. Lesson 1 CYP2 1.A 2.B 3.C 4.D A.9x 5 B.20x 5 C.20x 6 D.9x 6 A. Simplify (5x 2 )(4x 3 ).

9. Lesson 1 CYP2 1.A 2.B 3.C 4.D A.6xy 5 B.–6x 2 y 6 C.1x 3 y 5 D.–6x 3 y 5 B. Simplify 3xy 2 (–2x 2 y 3 ).

10. Key Concept 7-1b

11. Lesson 1 Ex3 Power of a Power Simplify ((2 3 ) 3 ) 2. Answer: = 2 18 or 262,144Simplify. ((2 3 ) 3 ) 2 = (2 3 ● 3 ) 2 Power of a Power = (2 9 ) 2 Simplify. = 2 9 ● 2 Power of a Power

12. 1.A 2.B 3.C 4.D Lesson 1 CYP3 A.4 7 B.4 8 C.4 12 D.4 10 Simplify ((4 2 ) 2 ) 3.

13. Key Concept 7-1c

14. Lesson 1 Ex4 GEOMETRY Find the volume of a cube with side length 5xyz. Answer: = 125x 3 y 3 z 3 Simplify. Power of a Product Volume = s 3 Formula for volume of a cube = (5xyz) 3 Replace s with 5xyz. = 5 3 x 3 y 3 z 3 Power of a Product

15. A.A B.B C.C D.D Lesson 1 CYP4 A.8p 3 q 3 B.24p 2 q 2 C.6p 2 q 2 D.8p 2 q 2 Express the surface area of the cube as a monomial.

16. Concept Summary 7-1d

17. Lesson 1 Ex5 Simplify [(8g 3 h 4 ) 2 ] 2 (2gh 5 ) 4 [(8g 3 h 4 ) 2 ] 2 (2gh 5 ) 4 = (8g 3 h 4 ) 4 (2gh 5 ) 4 Power of a Power = (8 4 )(g 3 ) 4 (h 4 ) 4 (2) 4 g 4 (h 5 ) 4 Power of a Product = 4096g 12 h 16 (16)g 4 h 20 Power of a Power = 4096(16)g 12 ● g 4 ● h 16 ● h 20 Commutative Property Answer: = 65,536g 16 h 36 Power of Powers Simplify Expressions

18. A.A B.B C.C D.D Lesson 1 CYP5 A.1728c 27 d 24 B.6c 7 d 5 C.24c 13 d 10 D.5c 7 d 21 Simplify [(2c 2 d 3 ) 2 ] 3 (3c 5 d 2 ) 3.