Algebra 2: New Groups 3rd 3 Period For Each Group Leader we need a balanced team of learning styles, so split up the rest of the numbers evenly.

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Algebra 2: New Groups 2nd B Period For Each Group Leader we need a balanced team of learning styles, so split up the rest of the numbers evenly.

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Lucas Marchand Lindsey Mason Danycia Riley Sarabeth Trinidad(Kinesthetic) (kinesthetic) (Visual/Auditory) (Visual)

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Algebra 2: New Groups 3rd B Period For Each Group Leader we need a balanced team of learning styles, so split up the rest of the numbers evenly.

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Evaluate nth Roots, Use Rational Exponents, and Apply Properties of Rational Exponents. GOALS: “”

Algebra 2: Notes 6.1 & 6.2:

What are the properties of exponents?

6.1 & 6.2 Example 1: Find the indicated real nth root(s) of a.

1. Rewrite as a radical 3 64

3 3 63 64 1 2

33 64 1 2 2 2 2 2 2 2. Find the prime factors of the # inside

3 6 1 23 3 364 1 2 1 2

3. Divide the power by the root

4. Simplify

3 64 4

1. Rewrite as a radical 6 729

666 729 3

6 6729 3 3 3 3 3 3 2. Find the prime factors of the # inside

6 16 6729 3 3

3. Divide the power by the root

4. Simplify

6 729 3

6.1 & 6.2 Example 2: Evaluate an expression w/rational exponents.

1. Get positive exponents 4 34 3

18

8

4 33

1

2

2. Find the prime factors of the base

4

1

23. Simplify powers

4. Simplify 4 3 18

16

1. Get positive exponent & write as a radical

4 3

43

18

8

433

1

2

2. Find the prime factors of the # inside

12 3 4

1 1

2 2

3. Multiply powers & divide the power by the root

4. Simplify

4 3 18

16

PS 6.1 pg.417 #7, 11, 27-45 odds

6.1 & 6.2 Example 3: Solve equations with nth roots.

1. Isolate exponent

62 1458

2 2

x

6 729x

2. Take the root of both sides.

66 6 729

3

x

x

34 12x

3 33

3

4 12

4 12

x

x

3

3

4 12

4 4

4 12

1.71

x

x

x

3. Solve for x

1. Isolate exponent

2. Take the root of both sides.

6.1 & 6.2 Example 4: Problem Solving with nth roots.

1. Write model for population

31.21

tP C

19 375 1.21P

2. Substitute for C & t.

250.82P 3. Simplify

PS 6.1 pg.417 #49-57 odds

6.1 & 6.2 Example 5: Use properties of exponents and radicals.

312 49 5 49

6 3 3 67 5 2 1 27 5 1 249 5

5 27 9 5 243 55 3 3

3192

3 3 64 4

6.1 & 6.2 Example 6: Write radicals in simplest form.

5 72 5 55 2 22 2 2 2 52 4

2 3 2 32 7 12 9 12

44 42 3 3 4 4 42 3 3 3

5 155 2 x 32x

1 2 4 2 10 236 m n 2 56m n

b.

a.

e.

d.

c.

6.1 & 6.2 Example 6: Write radicals in simplest form.

9 33

263

a a

bb

4 3 2 7 5

3

17

x zy

PS 6.2 pg.424 #7, 11, 15-25, 29, 35, 41-49, 53-61 odds

5 2 3 27x y z

2 2

46 2

a b

b b

2 2 2 24

48 2

a b a b

b b

5 510 6 4y y

2 1 4 2 1 43 4 7a b a b

g.

f.

i.

h.

j.