Post on 19-Jan-2016
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)