warm up 10/13 simplify each expression. 16,807 121 729 1. 7 3 7 2 3. (3 2 ) 3 2. 11 8 11 6 4. 5. 75...
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Warm Up 10/13
Simplify each expression.
16,807
121
729
1. 73 • 72
3. (32)3
2. 118
116
4.
5.
75
207
2 35
7
5 3
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Be seated before the bell rings
DESK
homeworkWarm-up (in your notes)
Agenda:
WarmupNotes 8.6
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NotebookTable of content
Page1
1
19)Add, subtract, multiply polynomials
20) Dividing Polynomials
21) Factor and find roots
22) Fundamental Theorem of Algebra
23)Graph of polynomials
24) Radical Expressions and Rational exponents
8.6 Radical Expressions and Rational exponents
HW ;
p.615(3-23 odd)
(35-55 odd)
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8.6 radical Expressions and Rational Exponents
1. Find all the square roots of 25
25 2 25x 5x 5x
5 32
2. Find all the fifth roots of 325 32x 2x 2x
3 64
3. Find all the cube roots of -643 64x 4x
4 6254. Find all the fourth roots of -625
4 625x x no solution
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n athe nth roots of a
Types of real roots
Case # of roots examples
index
odd 1 real root
even; + radicand
radicand
2 real roots
even; - radicand 0 real roots
Radicand =0 1 real root
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5. Find all real roots.
a. fourth roots of –256
negative - no real fourth roots.
Check It Out! Example 1
b. sixth roots of 1
positive - two real sixth roots. X = 1 and –1.
c. cube roots of 125
positive - one real cube root. X= 5.
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3 x x x
3x3
Simplifying Radical Expressions
6.
7.
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Simplify the expression. Assume that all variables are positive.
2 x
2x
4 416x
4 24 •4 x4
4 24 •x4
8. 9.
84
4 3
x
42
27
3x
10. 3 37 2x x
x3
3 9x
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n
ma n ma
5
38 53 8 53 8
52
32
10.
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Method 1 Evaluate the root first.
(4)1
6413
4
Write the expression in radical form, and simplify.
Method 2
4
13 64 13 64
3 64
11.
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Method 1.
(2)5
452
32
You try!
12.
Method 2
32
52 4 5
2 4
2 1024
6253413.
(5)3
125
34 625
125
34 625
4 244,140,625
Method 1. Method 2
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Writing Expressions by Using Rational Exponents
Simplify.
15 5 13
1312 Simplify.
14. 15.
4813
133
2197
m
mn na a m
mn na a
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Simplify.
16. 17.
3481
103
You try!
9310
1000
m
mn na am
mn na a
Simplify. 512
18.
24 5
mmn na a
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Rational exponents have the same properties as integer exponents
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Product of Powers.
Simplify each expression.
19.
Simplify.
Evaluate the Power.
72
49
Check Enter the expression in a graphing calculator.
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Simplify each expression.
1
4
6
20. 21. (–8)–
13
22.
1
–8 13
1
2 –
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Lesson Quiz:
Find all real roots.
–5, 51. fourth roots of 625
2. fifth roots of –243 –3
Simplify each expression.
2 4. 4y2
5. Write (–216) in radical form and simplify.23
6. Write using rational exponents. 5321
3. 84 256y
= 36 2
3 2163 521