Chapter 7

Section 4Rational Exponents

A rational exponent is another way to write a radical expression.

Like the radical form, the exponent form always indicates the principal root.

414

313

21

1616

2727

2525

FormExponent Form Radical

Simplify each expression.

31

31

21

21

31

10010 c)

55 b)

125 a)

If the numerator is not 1:

32 323

252525

:

Example

aaamnn mn

m

If the exponent is negative• Remember to put the base in the

denominator if it is not there already (or move it to the numerator if it is in the denominator)

33

3 5

35

99

:1

44

5 5

Example

xx

xxyy

c cdd

Write in radical form

35

-2.5

A) x

B) y

3- 8

.4

C) y

D) z

Write in exponential form

3

5 2

A)

B) b

a 3 2

3

C)

1D) y

x

Properties of Exponentsp. 381 (a nice chart)

When Multiplying like bases…add exponentsWhen Dividing like bases …subtract exponentsWhen taking a power to a power… multiply exponentsEverything in parenthesis gets the exponent

m n m na a a

nm m na a

or m m

n n nm

a aam a mb b

mm n

n

a aa

Simplest form always has only positive exponents

3

5

3.5

-32

Examples:

A) -32

B) 4

C) 25