MultDivideMonomials.notebook 1 September 18, 2014 Powers and Exponents Lesson objectives Teachers' notes 1) Power Rules 2) Multiplying and Dividing polynomials with monomials Multiplying binomials 3) Working with Negative Exponents 4) Multiplying Power to a power
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MultDivideMonomials.notebook
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September 18, 2014
Powers and Exponents
Lesson objectives Teachers' notes
1) Power Rules
2) Multiplying and Dividing polynomials with monomialsMultiplying binomials
3) Working with Negative Exponents
4) Multiplying Power to a power
MultDivideMonomials.notebook
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September 18, 2014
Teachers' notesLesson objectives
Subject:
Topic:
Grade(s):
Prior knowledge:
Mathematics
Powers and Exponents
Grade 8
Integers and Variables
Lesson notes:
8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 × 3–5 = 3–3 = 1/33 = 1/27.
MultDivideMonomials.notebook
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September 18, 2014
Multiplying and Dividing MonomialsBut what is a monomial?
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
MultDivideMonomials.notebook
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September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
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September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Constant: a monomial that is a real number.
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
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September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Constant: a monomial that is a real number. Example: 25
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
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September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Constant: a monomial that is a real number. Example: 25
17 c 8f2g 34
5t
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
8
September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Constant: a monomial that is a real number. Example: 25
17 c 8f2g 34
5t
No, the expression contains subtraction
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
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September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Constant: a monomial that is a real number. Example: 25
17 c 8f2g 34
5t
No, the expression contains subtraction
Yes, the expression is the PRODUCT of a number and more than a variable
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
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September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Constant: a monomial that is a real number. Example: 25
17 c 8f2g 34
5t
No, the expression contains subtraction
Yes, the expression is the PRODUCT of a number and more than a variable
Yes, the expression is a constant
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
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September 18, 2014
Monomials: a number, a variable, or product of a number and one or more variable(s) with nonnegative integer exponents.
Example: h2, x, 10
Constant: a monomial that is a real number. Example: 25
17 c 8f2g 34
5t
No, the expression contains subtraction
Yes, the expression is the PRODUCT of a number and more than a variable
Yes, the expression is a constant
No, variable can not be in the deniminator
Multiplying and Dividing MonomialsBut what is a monomial?
MultDivideMonomials.notebook
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September 18, 2014
Aim: What are the Laws of Exponents for Multiplication and Division?
Just like we can multiply two numbers together, we can also multiply two exponents (or two monomials) together. To do this, we follow the Product of Powers Rule.
Product of Powers Rule: To multiply exponents that have the same base, simply add the exponents.
am • an = am+n
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September 18, 2014
Aim: What are the Laws of Exponents for Multiplication and Division?
This can be seen if we actually count factors when multiplying exponents
75 • 74 =
It is very important to remember that bases have to beTHE SAME!!!!!!
= 79
9 factors
(7 • 7 • 7 • 7 • 7)
5 factors
(7 • 7• 7 • 7) •
4 factors
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Examples1) 52 • 5 2) x3 • x5 3) w6 • w15
When there is a coefficient (number in front of the variable) we multiply them together.
4) 3x2 • 4x5 5) 2x5 • 3x7 6) 2a3 • (8a4)
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September 18, 2014
Aim: What are the Laws of Exponents for Multiplication and Division?
Dividing exponents ... To divide exponents that have the same base, simply subtract the exponents. This is the Quotient of Powers Rule.
a9 ÷ a5 = a(9-5) = a4
a a a a a a a a aa a a a a
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September 18, 2014
Examples7) f8 8) g52
When there is a coefficient, we divide them. 9) 12x5 10) (2)5 • 34 • 57 11) 15n7
f3 g2
2x2 (2)2 • 3 • 54 3n4
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September 18, 2014
Homework ‐
WS p. 27 1‐10
11 & 12 are extra credit
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MultDivideMonomials.notebook
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September 18, 2014
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September 18, 2014
Aim: How do we multiply a monomial with a polynomial? How do we divide a
polynomial by monomial?
MultDivideMonomials.notebook
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September 18, 2014
Aim: How do we multiply a monomial with a polynomial? How do we divide a
polynomial by monomial?
To multiply a monomial by a polynomial:• Distribute• Follow the Laws of Exponents
1. Multiply the coefficients2. If the bases are the same keep the base and
add the exponents
2x(3x2 + 4x 6) =
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September 18, 2014
Aim: How do we multiply a monomial with a polynomial? How do we divide a
polynomial by monomial?
To divide a polynomial by a monomial:• Divide each piece of the numerator by the denominator• Divide the coefficients• Follow the Laws of Exponents
1. Divide the coefficients2. If the bases are the same keep the base and subtract the exponents