Write out on the board how to do them using radicals!!! The PP has how to solve using powers….you show how to use radicals!!!

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Algebra 2: Section 7.2

Properties of Rational Exponents

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Examples: Simplify

48. 6444 16 4 42 4

Alternate Method

4 62 4 44 22 2 42 4

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Rationalizing Denominator with Rational Exponents

Goal: Create an exponent in denominator that is a whole number

Base that you multiply top and bottom of fraction by must have exponent that adds to a whole number in the denominator

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Examples: Simplify

47

9. 8

4

4

7

8 Can’t have a radical in denominator!

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4 3

7

2

4 1

4 1

2

2 Rationalize: now we will have a fourth

power of 2 under the fourth root

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4 4

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2

4 14

2

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Adding & Subtracting Roots and Rational Exponents

Similar to combining like terms Radical parts must be EXACTLY ALIKE

– Same roots– Same numbers under the radical

May need to simplify radical

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Examples

3 3

4 410. 5 4 3 4

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42 4

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4How many 4 are there?

5 3

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Examples

3 311. 81 3Simplify the cube root of 81. May end up with like radicals

3 4 33 33 33 1 33 3 3

3 33 3 332 3

There is a one in front of this radical

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Examples

3 912. 27z

3 93 27 z9

3 3 33 z

33z

Usually easier to simplify variablesIn radicals by changing to rational exponents

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Examples

14 2 213. (16 )g h

1 4 2

2 2 216 g h2 116 g h

24g h

Multiply each exponent by one-half

Usually easier to think of numbers in termsOf radicals instead of rational exponents

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Examples

5

510

14.x

y

5

5

10

5

x

y2

x

y

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Examples

2

3

134

1815.

6

rs

r t

233

1

4

3rs t

r

Simplified 18/6and moved t to numeratorbecause of (-3) exponent

233343r s t

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4r

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Examples

4 9 14416. 12d e f

4 8 1 12 24 12d e e f fFactor out perfect 4th powers.(Powers that are divisible by 4)

4 8 12 1 24 4 12d e f e f

2 3 24 12de f ef

Use product property to rewrite order,so that terms in first radical are thosethat will simplify

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Examples

2

57

17.g

h

25

5 7

g

h

Factor out perfect 5th powers

25

5 5 2

g

h h

25

5 2

g

h h

2 5 35

5 52 3

g h

h h h

2 35

5 5

g h

h h

2 35 g h

h h

2 35

2

g h

h

Can’t have radical in denominator

Rationalize

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Homework

P.411

#43-75 odds

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Homework

P.411#42-74 evens