Rational Expon ents and Radicals

Rational Exponents

and

RadicalsBy: Jeffrey Bivin

Lake Zurich High School

[email protected]

Last Updated: December 11, 2007

Properties of rational Exponentsn aa n

1

mnnm

aa1

mn a

n ma nnm maa

1

21616 441

821616 3344

3

840961616 44 343

n mmn aa

Jeff Bivin -- LZHS

Are these equivalent?

77 xx

533 5 xx

353 5 xx

73 53 75 xx Jeff Bivin -- LZHS

Evaluate each

xx 2

xx 3 3

xx 4 4

xx 5 5

xx 6 6

Jeff Bivin -- LZHS

Evaluate7x

xxxx 222

xxxx 222

xxxx

xx3

Jeff Bivin -- LZHS

Now Consider7x

xx 32

xx 32

xx 3

2

xxxx 222

xx3

n mmn aa

Jeff Bivin -- LZHS

Evaluate

3 14x

3 23333 xxxxx

3 23 33 33 33 3 xxxxx

3 2xxxxx

3 24 xx

Jeff Bivin -- LZHS

Consider3 14x

3 24 xx

3 243 xx

3 24

3 3 xx 3 23 33 33 33 3 xxxxx

3 23333 xxxxx

3 14x

3 2xxxxx 3 24 xx

Jeff Bivin -- LZHS

One More3 14x

314

x3 212 xx

3 23 12 xx

32

312

xx

3 14x

324 xx

3 24 xx3 24 xx

Jeff Bivin -- LZHS

Evaluate5 332614 zyx

5 365155425 zzyyxx

5 34652 zyxzyx

5 3146

5 55

5 52

5 5 zyxzyx

Jeff Bivin -- LZHS

Evaluate

5 332614 zyx

5 34652 zyxzyx

Jeff Bivin -- LZHS

Evaluate

7 231434 zyx

7 26324 zxzyx

Jeff Bivin -- LZHS

Evaluate

4 291815 zyx

4 23743 zyxzyx

4 23734 zyxzxy

Don’t forget, even root – we

need to use absolute value

An even power can

come out of the absolute

value

Jeff Bivin -- LZHS

Evaluate: 3 144

3 211 322

144

722

98

32 23

3 24 32

3 182Jeff Bivin -- LZHS

Evaluate: 4000

1112 5252

4000

10040

104

22 52

35 52

1020

210

22 52

Jeff Bivin -- LZHS

Evaluate: 2791152 yx

yxyx 113413 232

1152

5762

2

1442

27927 32 yx

xyyx 224 134

288

212

222 32 42

Jeff Bivin -- LZHS

5 1419612 32 ba

5 1175 312 5832512 baba

5 1419639 322 ba

Simplify

5 44122312 3232 baba

5 4423 1212 baba

Jeff Bivin -- LZHS

53233

1523

Simplify

5363563

Jeff Bivin -- LZHS

3 43 3 22

3 223 2 2222

Simplify

33333 4424424

3 222

Jeff Bivin -- LZHS

Simplify

5337

57355432

Jeff Bivin -- LZHS

253916269233622

Simplify

359246233262

34523

759326183722

34522429212

Jeff Bivin -- LZHS

Simplify

3 1083 3 )108()1(

108

542

96

23

Jeff Bivin -- LZHS

32

3 1083 32 32

33 2 4323

Jeff Bivin -- LZHS

Simplify

2

2

4

2

2

2

2

1

2

1

Jeff Bivin -- LZHS

Simplify

32

6

2

6

Jeff Bivin -- LZHS

3

30

9

30

3

3

3

10

3

10

Simplify

Jeff Bivin -- LZHS

5

5

5

32

5

12

5

12

10

24

10

24

Simplify

5

152

25

152

Jeff Bivin -- LZHS

2

4

2

2

2

2

2

2

2

1

2

1 33 2

3 3

3 2

3 2

3 2

33

Simplify

Jeff Bivin -- LZHS

3

162

3

32

3

3

3

2

3

2 5

5 5

5 4

5 4

5 4

5

5

5

Simplify

Jeff Bivin -- LZHS

zy

zyx

zy

zyx 6 24

6 66

6 24

6 24

6 24

6 42

6

642

zy

zy

zy

x

zy

x

Simplify

Jeff Bivin -- LZHS

2

20

2

25 5

5 5

5 2

5 2

5 2

5 3

5

5

2

2

2

5

8

5

Simplify

Jeff Bivin -- LZHS

4

8

2

2

2

2

2

2

2

1

32

1 4

2

4 3

4 8

4 3

4 3

4 3

4 54

Simplify

Jeff Bivin -- LZHS

Express using Rational Exponents

21

77 51

225

323 2 xx

Jeff Bivin -- LZHS


23

696 9 aaa

Jeff Bivin -- LZHS


8 6524 yx

86

85

81

83

32 yx 43

8 653 32 yx

Jeff Bivin -- LZHS

Express in Simplest Radical From

52

x 5 2x

Jeff Bivin -- LZHS


32

64 3 264

3 262

1622 43 12

Jeff Bivin -- LZHS


47

x4 7x4 3xx

Jeff Bivin -- LZHS


310

35

yx

31105 yx

3 233 105 yxyxyx

Jeff Bivin -- LZHS


27

45

32

zyx1242

1215

128

zyx12 638312 42158 zyxzyzyx

Jeff Bivin -- LZHS


3 2616 yx

2131

2616 yx 612616 yx

6 2616 yx 6 2442 yxyx

2

Jeff Bivin -- LZHS


41

31

21

2110

yx

24 2110 yx

Jeff Bivin -- LZHS

2412110 yx

4 3 2110 yx


5 11375 yxyx

5121

11375 yxyx

1012113575 yxyx

10

5

10

2


1012113575 yxyx

1012263525 yxyx

10 5731 yx 10 7153 yxyx


5 11375 yxyx

10 22610 3525 yxyx

10 2263525 yxyx

10 7153 yxyx


12 5 21122110 yxyx

Jeff Bivin -- LZHS

4 33

5 742110 yxyx

12 10 422410550 yxyx

2

120 14774 yx 120 2774 yxy


21

126

xx

Jeff Bivin -- LZHS

x

12 6x

4 32 zyx


Jeff Bivin -- LZHS

8 624 zyx


Jeff Bivin -- LZHS

12 694 zyx

12 694 zyx

6 2442 yxyx

3 242 yxyx


Jeff Bivin -- LZHS


Jeff Bivin -- LZHS

6 246 yx

6 246 yx


Jeff Bivin -- LZHS

3 1222 yx

3 24 yx

6 2416 yx remember

16 = 24

6 2442 yx

7

23

223239

23

23

23

23

1

Simplify

Jeff Bivin -- LZHS

11

5312

11

543

5545416

543

54

54

54

3

Simplify

Jeff Bivin -- LZHS

3

71

6

712

7771

712

71

71

71

2

Simplify

Jeff Bivin -- LZHS

3321

332

332324

332

32

32

32

3

Simplify

Jeff Bivin -- LZHS

Rational Expon ents and Radicals

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