7 1 Multiplication Properties of Exponents 7 1

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7 -1: Multiplication Properties of Exponents

7 -1: Multiplication Properties of Exponents

7 -1: Multiplication Properties of Exponents • Monomial: A number, variable, or the product

7 -1: Multiplication Properties of Exponents • Monomial: A number, variable, or the product of a number and one or more variables • Constant: A monomial that is a real number • Example 1: Identifying monomials ▫ Determine whether each expression is a monomial. Explain. ▫ 10 �Yes; it’s a constant, so it’s a monomial ▫ f + 24 �No; the expression has addition, so it has more than one term ▫ h 2 �Yes; it’s the product of variables ▫ j �Yes; single variables are monomials

7 -1: Multiplication Properties of Exponents • Your Turn ▫ Determine whether each expression

7 -1: Multiplication Properties of Exponents • Your Turn ▫ Determine whether each expression is a monomial. Explain. ▫ -x + 5 �No; the expression has more than one term ▫ 23 abcd 2 �Yes; product of number and variables ▫ �Yes; product of number and variables

7 -1: Multiplication Properties of Exponents • Product of Powers ▫ To multiply two

7 -1: Multiplication Properties of Exponents • Product of Powers ▫ To multiply two powers that have the same base, add their exponents ▫ Examples �b 3 ● b 5 = b 3+5 = b 8 �g 4 ● g 6 = g 4+6 = g 10

7 -1: Multiplication Properties of Exponents • Example 2: Simplify each expression ▫ (6

7 -1: Multiplication Properties of Exponents • Example 2: Simplify each expression ▫ (6 n 3)(2 n 7) ▫ ▫ = (6 ● 2)(n 3 ● n 7) = (6 ● 2)(n 3+7) = 12 n 10 ▫ (3 pt 3)(p 3 t 4) = (3 ● 1)(p ● p 3)(t 3 ● t 4) ▫ = (3 ● 1)(p 1+3)(t 3+4) ▫ = 3 p 4 t 7

1) Simplify (5 x 2)(4 x 3) 1. 9 x 5 2. 20 x

1) Simplify (5 x 2)(4 x 3) 1. 9 x 5 2. 20 x 5 3. 20 x 6 4. 9 x 6

2) Simplify 3 xy 2(-2 x 2 y 3) 1. 6 xy 5 2.

2) Simplify 3 xy 2(-2 x 2 y 3) 1. 6 xy 5 2. -6 x 2 x 6 3. 1 x 3 y 5 4. -6 x 3 y 5

7 -1: Multiplication Properties of Exponents • Power to a power ▫ When an

7 -1: Multiplication Properties of Exponents • Power to a power ▫ When an exponent is on the outside of parenthesis, multiply exponents ▫ Examples �(b 3)5 = b 3● 5 = b 15 �(g 6)7 = g 6● 7 = g 42

7 -1: Multiplication Properties of Exponents • Example 3: Simplify each expression ▫ [(23)2]4

7 -1: Multiplication Properties of Exponents • Example 3: Simplify each expression ▫ [(23)2]4 ▫ = 23● 2● 4 = 224 ▫ (-2 f 2 g 3 h 2)3 ▫ ▫ = (-2)3(f 2)3(g 3)3(h 2)3 = (-2)3(f 2● 3)(g 3● 3)(h 2● 3) = -8 f 6 g 9 h 6

3) Simplify [(42)2]3 1. 47 2. 48 3. 412 4. 410

3) Simplify [(42)2]3 1. 47 2. 48 3. 412 4. 410

4) Simplify (5 k 2)3 1. 125 k 6 2. 125 k 5 3.

4) Simplify (5 k 2)3 1. 125 k 6 2. 125 k 5 3. 5 k 6 4. 5 k 8

Leader Board 4 3 3 3 Isiah Hanlan Madison Roney Robert Porter Alexander Vendrell

Leader Board 4 3 3 3 Isiah Hanlan Madison Roney Robert Porter Alexander Vendrell 3 Anya Augin

7 -1: Multiplication Properties of Exponents • Assignment ▫ Page 394 – 395 ▫

7 -1: Multiplication Properties of Exponents • Assignment ▫ Page 394 – 395 ▫ 1 – 15 & 21 – 37 (odds)

7 -1: Multiplication Properties of Exponents Day 2

7 -1: Multiplication Properties of Exponents Day 2

7 -1: Multiplication Properties of Exponents • To simplify a monomial expression ▫ Simplify

7 -1: Multiplication Properties of Exponents • To simplify a monomial expression ▫ Simplify any power to a power ▫ Simplify any product of powers • Example 3: Simplify (3 xy 4)2[(-2 y)2]3 ▫ ▫ ▫ (3 xy 4)2[(-2 y)2]3 (3 xy 4)2(-2 y)6 32 x 2 y 8(-2)6 y 6 9 x 2 y 8(64)y 6 576 x 2 y 14 Power to power Simplify numers Product of powers

5) Simplify (4 x 2 y)(2 xy 2 z 3)3 1. 8 x 5

5) Simplify (4 x 2 y)(2 xy 2 z 3)3 1. 8 x 5 y 7 z 9 2. 32 x 6 y 6 z 9 3. 32 x 5 y 7 z 9 4. 24 x 5 y 7 z 9

6) Simplify [(2 c 2 d 3)2]3(3 c 5 d 2)3 1. 1728 c

6) Simplify [(2 c 2 d 3)2]3(3 c 5 d 2)3 1. 1728 c 27 d 24 2. 6 c 7 d 5 3. 24 c 13 d 10 4. 5 c 7 d 21

Leader Board 3 3 2 2 Jemikah Harrell Brandon Hulme Isiah Hanlan Shannon Glessner

Leader Board 3 3 2 2 Jemikah Harrell Brandon Hulme Isiah Hanlan Shannon Glessner 2 Andrea Kakas

7 -1: Multiplication Properties of Exponents • Assignment ▫ Page 394 – 395 ▫

7 -1: Multiplication Properties of Exponents • Assignment ▫ Page 394 – 395 ▫ 17 – 19 & 41 – 55 (odds)