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WRITING RADICALS IN RATIONAL WRITING RADICALS IN RATIONAL FORMFORM

Section 10.2

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DEFINITIONSDEFINITIONS

Base: The term/variable of which is being raised upon

Exponent: The term/variable is raised by a term. AKA Power

ma BASEBASE

EXPONENTEXPONENT

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THE EXPONENTTHE EXPONENT

ma 322 2 2 2 3 2 2 2

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NTH ROOT RULENTH ROOT RULE

• M is the power (exponent)• N is the root• A is the base

/m

m n na a

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RULESRULES

Another way of writing is 251/2. is written in radical expression form.251/2 is written in rational exponent form.

Why is square root of 25 equals out of 25 raised to ½ power?

25

25

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EXAMPLE 1EXAMPLE 1

Evaluate 43/2 in radical form and simplify.

/m

m n na a

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EXAMPLE 1EXAMPLE 1

Evaluate 43/2 in radical form and simplify.

/m

m n na a

33/24 4

3 34 2

8

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EXAMPLE 2EXAMPLE 2Evaluate 41/2 in radical form and

simplify.

2

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YOUR TURNYOUR TURNEvaluate (–27)2/3 in radical form and

simplify.

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EXAMPLE 3EXAMPLE 3

Evaluate –274/3 in radical form and simplify.

/m

m n na a

43 27

Hint: Remember, the negative is OUTSIDE of the base

81

Use calculator to check

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EXAMPLE 4EXAMPLE 4Evaluate in radical form and simplify.

35 4 1x

3/54 1x

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NTH ROOT RULENTH ROOT RULE

• M is the power (exponent)• N is the root• A is the base

DROP AND SWAP

//

1mm n n

m na a

a

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EXAMPLE 5EXAMPLE 5

Evaluate (27)–2/3 in radical form and simplify.

1

9

2/327

23 27

23

1

27

21

3

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EXAMPLE 6EXAMPLE 6

Evaluate (–64)–2/3 in radical form and simplify.

1

16

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YOUR TURNYOUR TURN

Evaluate in radical form and simplify.

1 1

1 1

25 36

36 25

1/225

36

6

5

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PROPERTIES OF EXPONENTSPROPERTIES OF EXPONENTS

Product of a Power:

Power of a Power:

Power of a Product:

Negative Power Property:

Quotient Power Property:

m n m na a a ( ) m n m na a

( ) m m mab a b( )

1nn

aa

mm n

n

aa

a

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EXAMPLEEXAMPLE 7 7Simplify

• Saying goes: BASE, BASE, ADD

If the BASES are the same, ADD the powersm n m na a a

4 52 2

92

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EXAMPLE 8EXAMPLE 8Simplify 1/2 1/3x x

5/6x

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YOUR TURNYOUR TURNSimplify 3/5 1/4x x

17/20x

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EXAMPLE 9EXAMPLE 9Simplify

• Saying goes: POWER, POWER, MULTIPLY

If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES

( ) m n m na a

542

202

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EXAMPLE 10EXAMPLE 10Simplify

( ) m m mab a b

52/52x

232x

/ ( / )( )52 5 5 2 5 52 2x x

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YOUR TURNYOUR TURNSimplify 41/4 2/33x y

2/3

81x

y

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EXAMPLE 11EXAMPLE 11Simplify

• Saying goes: When dividing an expression with a power, SUBTRACT the powers.

m

m nn

aa

a

1/3

4/3

7

7

1

7

// /

/

1 31 3 4 3

4 3

77

7

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EXAMPLE 12EXAMPLE 12Simplify

3

x

x

1/6x

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EXAMPLE 13EXAMPLE 13Simplify

33 4

5

xx x

x

13/60x