1. 8.1 Multiplying Exponents

2. Begin 2 column notes… table on page 410 s = mph 1/20 s 2 = breaking distance Algebra 1 Glencoe Mathematics 8-1 Multiplying Monomials pages 410-415 What You’ll Learn Multiply monomials Simplify expressions involving powers of monomials Why Does doubling speed quadruple braking distance?

3. Continue 2 column notes… Vocabularymonomial ; constant Multiplying Monomials constant – monomials that are real number monomial monomial – a number, a variable, or a product of a number and one or more variables constant

4. Stop: Let’s look at Example 1 ExpressionMonomial? -5 p+q x Yes No – no +’s No – no ÷ ’s

5. Continue 2 column notes… Example 1 p. 410 Identifying Monomials Are these monomials: -5 p+q x c/d abc 8 /5 yes no- no “+” or “-“ allowed yes no variable in denominator yes Study Tip p. 410 How do you read x n ? x to the nth power

6. Continue 2 column notes… Key Concept Product of Powers Words To multiply two powers that have the same base, add the exponents. Symbols a m.a n = a m + n Examplea 4.a 12 = a 4 + 12 or a 16

7. Stop: Let’s look at Example 2: Simplify each expression. B) A)

8. Continue 2 column notes… Example 2 p. 411 Simplify a. (5x 7 )(x 6 ) b. (4ab 6 )(-7ab 2 b 3 ) a.(5x 7 )(x 6 )=(5)(1)(x 7 x 6 )=(5∙1)(x 7+6 )=5x 13 b. (4ab 6 )(-7ab 2 b 3 )=(4)(-7)(a∙a 2 )(b 6 ∙b 3 ) =(-28)(a 1+2 )(b 6+3 )=-28a 3 b 9

9. Continue 2 column notes… Study Tip p. 411 What power does x have? A variable without an exponent has power 1. Key Concept Power of a Power WordsTo find the power of a number, multiply the exponents. Symbols(a m ) n = a m ∙ n Example(k 5 ) 9 = k 5. 9 or k 45 Powers of Monomials

10. Stop. Lets look at Example 3: Simplify

11. Continue 2 column notes… Example 3 p. 411 Power of a Power Simplify [(3 2 ) 3 ] 2 [(3 2 ) 3 ] 2 =(3 2∙3 ) 2 =3 6∙2 =312 or 531,441 Key Concept Power of a Product WordsTo find the power of a product, find the power of each factor and multiply. Symbols(ab) m = a m b m Example (-2xy) 3 = (-2) 3 x 3 y 3 or -8x 3 y 3

12. STOP. Let’s look at Example 4: Express the area of the square as a monomial. 4ab

13. Continue 2 column notes… Study Tip p 412 How can you combine the Power of a Power and Power of a Product Rules? Sometimes rules for Power of a Power and Power of a Products are combined in one rule: (a m b n ) p =a mp b np. Example 4 p. 412 Find the area of a square if s=4ab. Area = s 2 =(4ab) 2 =4 2 a 2 b 2 =16a 2 b 2

14. Continue 2 column notes… Concept Summary Simplifying Monomial Expressions each base appears exactly once no powers of powers all fractions are in simplest form

15. STOP. Let’s look at Example 5: Simplify

16. Continue 2 column notes… Example 5 p. 412 Simplify Expressions Simplify ((1/3)xy 4 ) 2 [(-6y) 2 ] 3 ((1/3)xy 4 ) 2 [(-6y) 2 ] 3 =((1/3)xy 4 (-6y) 6 =(1/3) 2 x 2 (y 4 ) 2 (-6) 6 y 6 =(1/9)x 2 (y 8 )(46,656)y 6 =(1/9) (46,656)x 2 (y 8 )y 6 =5184 x 2 y 14

17. Continue 2 column notes… Homework: p 413 # 15 – 45odd

18. Do Homework on your 2 column notes…here’s the format 1)Give example of an expression that can be simplified using each property. Then simplify. a) Product of Powers b) Power of a Power c) Power of a Product a)Your ANSWER b)Your ANSWER c) Your ANSWER