7-1: Multiplication Properties of Exponents

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▫ h2

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 is a

monomial. Explain.▫-x + 5

No; the expression has more than one term▫23abcd2

Yes; product of number and variables▫

Yes; product of number and variables

2

2

xyz

7-1: Multiplication Properties of Exponents

•Product of Powers▫To multiply two powers that have the same

base, add their exponents▫Examples

b3 ● b5 = b3+5 = b8

g4 ● g6 = g4+6 = g10

7-1: Multiplication Properties of Exponents

•Example 2: Simplify each expression▫(6n3)(2n7)▫(6n3)(2n7) = (6 ● 2)(n3 ● n7)▫ = (6 ● 2)(n3+7)▫ = 12n10

▫(3pt3)(p3t4)▫(3pt3)(p3t4) = (3 ● 1)(p ● p3)(t3 ● t4)▫ = (3 ● 1)(p1+3)(t3+4)▫ = 3p4t7

1) Simplify (5x2)(4x3)

1 2 3 4

0% 0%

10%

90%1. 9x5

2. 20x5

3. 20x6

4. 9x6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

2) Simplify 3xy2(-2x2y3)

1 2 3 4

10%

90%

0%0%

1. 6xy5

2. -6x2x6

3. 1x3y5

4. -6x3y5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

7-1: Multiplication Properties of Exponents

•Power to a power▫When an exponent is on the outside of

parenthesis, multiply exponents▫Examples

(b3)5 = b3●5 = b15

(g6)7 = g6●7 = g42

7-1: Multiplication Properties of Exponents

•Example 3: Simplify each expression▫[(23)2]4

▫[(23)2]4 = 23●2●4

▫ = 224

▫(-2f2g3h2)3

▫(-2f2g3h2)3 = (-2)3(f2)3(g3)3(h2)3

▫ = (-2)3(f2●3)(g3●3)(h2●3)▫ = -8f6g9h6

3) Simplify [(42)2]3

1 2 3 4

5%0%

90%

5%

1. 47

2. 48

3. 412

4. 410

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

4) Simplify (5k2)3

1 2 3 4

10%5%

70%

15%

1. 125k6

2. 125k5

3. 5k6

4. 5k8

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

Leader Board4 Isiah Hanlan

3 Madison Roney

3 Robert Porter

3 Alexander Vendrell

3 Anya Augin

7-1: Multiplication Properties of Exponents

•Assignment▫Page 394 – 395▫1 – 15 & 21 – 37 (odds)

7-1: Multiplication Properties of ExponentsDay 2

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 (3xy4)2[(-2y)2]3

▫(3xy4)2[(-2y)2]3 Power to power▫(3xy4)2(-2y)6 Power to power▫32x2y8(-2)6y6 Simplify numers▫9x2y8(64)y6 Product of

powers▫576x2y14

5) Simplify (4x2y)(2xy2z3)3

1 2 3 4

26%

16%

42%

16%

1. 8x5y7z9

2. 32x6y6z9

3. 32x5y7z9

4. 24x5y7z9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

6) Simplify [(2c2d3)2]3(3c5d2)3

1 2 3 4

58%

0%

26%

16%

1. 1728c27d24

2. 6c7d5

3. 24c13d10

4. 5c7d21

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23

Leader Board3 Jemikah Harrell

3 Brandon Hulme

2 Isiah Hanlan

2 Shannon Glessner

2 Andrea Kakas

7-1: Multiplication Properties of Exponents

•Assignment▫Page 394 – 395▫17 – 19 & 41 – 55 (odds)