Unit: Radical Functions 7-4: Rational Exponents

Essential Question:

Explain the meaning of using radical expressions

mna

Another way to write a radical expression is to use a radical exponent.

Examples:

Radical Form

Exponent Form

=

=

=

253 274 16

122513271416

Rational Exponents can be simplified just like their radical counterparts.

Examples:

13 3125 125

5

1 12 25 5 5 5

5

1 13 3 3 3

3

10 100 10 100

1000

10

YOUR TURNSimplify

1416

1 12 22 21 12 22 8

4 16 2 1 12 22 2

1 12 22 8 16 4

Note that: 1) Like variables, you can add exponents when the base is the same 2) You can multiply bases when the exponent is the same

A rational exponent may have a numerator other than 1. The property (am)n = amn shows how to rewrite such an expression.

or

Basically, the numerator is the power a number is being raised to. The denominator is the root a number is being taken to.

13 1 22 23 3 325 25 25 25

3 1 12 2 2

3 3325 25 25 25

We can convert between the two forms Write the exponential expression in radical form:

Write the radical expressions in exponential form:

35

35 3 5x x or x

52

52

2.555

1 1 1y y or

y y y

323a a

25

25 b b

YOUR TURN Write the exponential expression in radical form:

Write the radical expressions in exponential form:

0.4z38y

25

25 2 5z z or z

38

338 8

1 1 1or

y y y

3 2x

3y23x

32y

Simplifying Numbers with Radical ExponentsAll the properties of integer exponents also

apply to rational exponents.See page 381 in your books for a summary.Examples:

35

35

3

32 32

2

8

72

72

3.5

7 7

14 4

4

1 1

241

128

YOUR TURN

3225

3532

45( 32)

32

3 3

1 1 1 1

5 12525 25

3 35 32 2 8

4 45 32 ( 2) 16

Writing in simplest form:

3 3 34 4 4

34

88

6 63

4

6 63

6

16 16

1 1

16 16

1 1

2 8

8

y y

y y

y y

y

YOUR TURNSimplify

13158x

1 13 3

13

15

5

53

5 5

8

1

81 1

81 1 1

2 2

x

x

x

x x

AssignmentPage 388 - 3891 – 25 & 31 – 49Odd problemsShow work