topic 6.2.1
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Rules of Exponents. Topic 6.2.1. Lesson 1.1.1. Topic 6.2.1. Rules of Exponents. California Standards: - PowerPoint PPT PresentationTRANSCRIPT
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Topic 6.2.1Topic 6.2.1
Rules of ExponentsRules of Exponents
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Lesson
1.1.1
California Standards:2.0 Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students solve multistep problems, including word problems, by using these techniques.
What it means for you:You’ll multiply and divide algebraic expressions using the rules of exponents.
Rules of ExponentsRules of ExponentsTopic
6.2.1
Key words:• exponent
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Lesson
1.1.1
You learned about the rules of exponents in Topic 1.3.1.
Rules of ExponentsRules of ExponentsTopic
6.2.1
In this Topic, you’ll apply those same rules to monomials and polynomials.
We’ll start with a quick recap of the rules of exponents to make sure you remember them all.
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1) xa·xb = xa+b 2) xa ÷ xb = xa–b (if x 0)
3) (xa)b = xab 4) (cx)b = cbxb
5) x0 = 1 6) x–a = (if x 0)
7)
xa
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Lesson
1.1.1
Use the Rules of Exponents to Simplify Expressions
Rules of ExponentsRules of ExponentsTopic
6.2.1
These are the same rules you learned in Chapter 1, but this time you’ll use them to simplify algebraic expressions:
Rules of Exponents
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(–2x2m)(–3x3m3)
= (–2)(–3)(x2)(x3)(m)(m3)
= 6x2+3·m1+3
= 6x5m4
Rules of ExponentsRules of Exponents
Example 1
Topic
6.2.1
Simplify the expression (–2x2m)(–3x3m3).
Solution
Solution follows…
Put all like variables together
Use Rule 1 and add the powers
Rule 1) xa·xb = xa+b
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(3a2xb3)2
= 32·a2·2·x2·b3·2
= 9a4x2b6
Rules of ExponentsRules of Exponents
Example 2
Topic
6.2.1
Simplify the expression (3a2xb3)2.
Solution
Solution follows…
Use Rules 3 and 4
Rule 3) (xa)b = xab
Rule 4) (cx)b = cbxb
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= 2xm2
Rules of ExponentsRules of Exponents
Example 3
Topic
6.2.1
Solution
Solution follows…
From Rule 5, anything to the power 0 is 1
Simplify the expression .
Separate the expression into parts that have only one variable
=
= Use Rule 2 and subtract the powers
Rule 2) xa ÷ xb = xa–b (if x 0) Rule 5) x0 = 1
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1. –3at(4a2t3) 2. (–5x3yt2)(–2x2y3t)
3. (–2x2y3)3 4. –2mx(3m2x – 4m2x + m3x3)
5. (–3x2t)3(–2x3t2)2 6. –2mc(–3m2c3 + 5mc)
Simplify each expression.
Lesson
1.1.1
Guided Practice
Rules of ExponentsRules of ExponentsTopic
6.2.1
Solution follows…
(–3 • 4)(a • a2)(t • t3)= –12a(1 + 2)t(1 + 3) (Rule 1)= –12a3t4
(–5 • –2)(x3 • x2)(y • y3)(t2 • t)= 10x(3 + 2)y(1 + 3)t(2 + 1) (Rule 1)= 10x5y4t3
(–2)(1 • 3)x(2 • 3)y(3 • 3) (Rule 3)= (–2)3x6y9
= –8x6y9
–2mx(–m2x + m3x3)= 2m(1 + 2)x(1 + 1) – 2m(1 + 3)x(1 + 3) (Rule 1)= 2m3x2 – 2m4x4
((–3)3x(2 • 3)t3)((–2)2x(3 • 2)t(2 • 2)) (Rule 3)= (–27x6t3)(4x6t4) = –108x(6 + 6)t(3 + 4) (Rule 1)= –108x12t7
6m(1 + 2)c(1 + 3) – 10m(1 + 1)c(1 + 1) (Rule 1)= 6m3c4 – 10m2c2
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Simplify each expression.
Lesson
1.1.1
Guided Practice
Rules of ExponentsRules of ExponentsTopic
6.2.1
Solution follows…
7. 8.
9. 10.
= 5m(3 – 2)n(8 – 3)z(6 – 1) (Rule 2)= 5mn5z5
= (14 ÷ 4)a(2 – 7)b(4 – 4)c(8 – 0) (Rule 2)
= a–5c8 (Rule 5) = (Rule 6)
= (12 ÷ 8)j(8 – 2)k(–8 – –10)m(–1 – 4) (Rule 2)
= j 6k2m–5 = (Rule 6)
= (16 ÷ 32)b(9 – 5 • 2)a(4 – 3 • 2)c(–1 • 2)j4 (Rule 2)
= b–1a–2c–2j4 = (Rule 6)
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1. 2.
3. 4a2(a2 – b2) 4. 4m2x2(x2 + x + 1)
5. a(a + 4) + 4(a + 4) 6. 2a(a – 4) – 3(a – 4)
7. m2n3(mx2 + 3nx + 2) – 4m2n3
8. 4m2n2(m3n8 + 4) – 3m3n10(m2 + 2n3)
Simplify.
Rules of ExponentsRules of Exponents
Independent Practice
Solution follows…
Topic
6.2.1
4a4 – 4a2b2
a2 + 8a + 16
m3n3x2 + 3m2n4x – 2m2n3
2a2 – 11a + 12
m5n10 + 16m2n2 – 6m3n13
4m2x4 + 4m2x3 + 4m2x2
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9. 10.
11. 12.
Simplify.
Rules of ExponentsRules of Exponents
Independent Practice
Solution follows…
Topic
6.2.1
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13. m?(m4 + 2m3) = m6 + 2m5
14. m4a6(3m?a8 + 4m2a?) = 3m7a14 + 4m6a9
Find the value of ? that makes these statements true.
Rules of ExponentsRules of Exponents
Independent Practice
Solution follows…
Topic
6.2.1
? = 2
? = 3
? = 4 ? = 7
15. 16.
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Topic
6.2.1
Round UpRound Up
Rules of ExponentsRules of Exponents
You can apply the rules of exponents to any algebraic values.
In this Topic you just dealt with monomials, but the rules work with expressions with more than one term too.