Radicals Rational Exponents

RadicalsRational Exponents

Target Goals: Write expressions with rational exponents in simplest radical form and vice versa;

Evaluate expressions in either exponential or radical form

Opener – Simplify each of the following using your exponent rules from the last chapter.

2 3x x 5x3 7x x 4x

6

2

xx

4x

2

9

xx

7x 7

1x

1 25 5x x

35x

1 16 3x x

1 26 6x x

36x

12x

58

14

x

x

5 18 4x

5 28 8x

38x

Opener – Simplify each of the following using your exponent rules from the last chapter.

42x 8x

23x 6x

312x

32x

13 64x

324x

18x

6

1x

Rational exponents are FRACTION EXPONENTS.

RATIONAL EXPONENTS:

an a nb b

Write the following in radical form.16Ex 1) x 6 x

74Ex 2) d 74 d

Write the following in exponential form.

4Ex 3) z14z 3 5Ex 4) d

53d

An expression with rational exponents is simplified when all of the following conditions are met: It has no negative exponents. It has no exponents that are not positive

integers in the denominator (i.e., no fraction exponents in the denominator).

It is not a complex fraction (i.e., fractions within fractions).

The index of any remaining radical is the least number possible (i.e., the fraction exponent is as simplified as possible).

Evaluate each expression/Simplify:14Ex 5) 81

14

1

81

4

181

4

13 3 3 3

13

14

1

81

1

4 4

1

3 14

4

1

3

13

1

4 43

1313

Evaluate each expression/Simplify:15Ex 6) 3125

15

1

3125

5

13125

5

15 5 5 5 5

15

1

5 5

1

5

15

1

5 55

15 15

Evaluate each expression/Simplify:23Ex 7) 216

23 36 26 36

3

8 82 32 838Ex 8) 256

1 94 4Ex 9) p p

104p

52p

Evaluate each expression/Simplify:45Ex 10) r

45

1

r

15

15

r

r

15rr

5 4

1

r

5

5

rr

5

5 5

r

r

5 rr

15rr

Simplify each expression:4 27Ex 11)

3

14

12

27

3

1

3 4

12

3

3

34

12

3

3

3 14 23

3 24 43

143 4 3

3 6Ex 12) 64z1 63 364 z

613 334 z 24z

Simplify: 12

12

2Ex 13) 2

y

y

22

yy

22

yy

2 2 42 2 4

y y yy y y

4 44

y yy

124 44

y yy

Multiply by the conjugate!!