1. Topic-
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| Multiplying Powers with the Same Base |
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2. Content-
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| Durig this lesson, students will be introduced to multiplying powers
with the same base including those with rational exponents. Ration
exponents are fractional powers. |
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3. Goals: Aims/Outcomes-
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EQ: How can you simplify expressions involving exponents?
N.RN.1 Explain how the definition of the meaning of rational exponents
follows from extending the properties of integer exponents to those
values, allowing for a notation for radicals in terms of rational
exponents.
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4. Objectives-
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1. Students will be able to explain rational expressions.
2. Students will be able to simplify expressions by multiply powers
with the same base, including those with rational exponents.
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5. Materials and Aids-
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1. Paper
2. Pencil
3. Overhead/White Board/Projector
4. Calculator
5. Worksheet |
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6. Procedures/Methods-
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A. Introduction-
Who can fill in the blank?
1. 3^2 * 3^2 = 3*3*3*3 = 3^4 = 3^(2+_)
2. 4^3 * 4^2 = 4*4*4*4*4 = 4^_ = 4^(_+_)
3. 6^3 * 6^3 = _ = 6^_ = 6^(_+_)
Are we seeing a pattern???
What is it? |
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B. Development-
PART A
*** When you are multiplying, and the bases are the same, ADD the
exponents.
*** x^m * x^n = x^(m+n) (PROOF)
1. x^3 * x^4 = (x*x*x)*(x*x*x*x) = x^7
(When in doubt, expand the terms)
2. 3x^3 * x^6 = 3x^9
(Bases are the same so add the exponents)
(Multiply the coefficients)
3. a^3(a^-4)(a^6) = a^(3+-4+6) = a^5
(Be careful when adding negative exponents)
4. (x^2 y^3)(x^4 y) = x^6 y^4
(Be sure to add ONLY the exponents for the bases that are the SAME)
5. rs(4r + 2s) = 4 r^2 s + 2 r s^2
(By the Distributive Property, rs is multiplie times EACH term inside
the parentheses)
(Add the exponents of the same bases in each multiplication)
6. 4z^5 * 9z^12 = 36z^-7 (What's wrong?) = 36/z^7
PART B
***Exponents can also be expressed as fractions.
*** Fractional exponents are called rational exponents.
*** x^(a/b) = (b|x)^a
(The denominator of the exponents becomes the power of the root)
1. 16^(1/4) = (4|16)^1 = (what*what*what*what = 6) = (2)^1 = 2
2. 8^(4/3) = (3|8)^4 = (2)^4 = 16 |
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C. Practice-
PART A
1. 11^4 * 11^3 = 11^7 = 19,487,171
2. 2^4 * 2 * 2^(-3) = 4
3. c^4 * d^(-3) * c^2 = c^6 / d^3
4. (2y^3)(7x^2)(2y^4) = 28 x^2 y^7
PART B
1. 8^(1/3) = 2
2. 25^(3/2) = 125
3. n^(1/3) * n^(4/3) = n^(5/3) |
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D. Independent Practice-
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E. Accommodations (Differentiated Instruction)-
ELL
1. Visuals
2. Show with hands
3. Write key information on overhead for students to copy |
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F. Checking for understanding-
1. Discussion during lecture
2. Evaluation during practice
3. Observations during independent practice |
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G. Closure-
1. Ask about the key things we learned today
2. Brief preview to next lesson |
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