WRITING RADICALS IN RATIONAL FORM Section 10 2

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WRITING RADICALS IN RATIONAL FORM Section 10. 2 11/30/2020 2: 24 PM 10. 2

WRITING RADICALS IN RATIONAL FORM Section 10. 2 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 1

DEFINITIONS EXPONENT BASE Base: The term/variable of which is being raised upon Exponent: The

DEFINITIONS EXPONENT BASE Base: The term/variable of which is being raised upon Exponent: The term/variable is raised by a term. AKA Power 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 2

THE EXPONENT 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 3

THE EXPONENT 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 3

NTH ROOT RULE • M is the power (exponent) • N is the root

NTH ROOT RULE • M is the power (exponent) • N is the root • A is the base 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 4

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

RULES 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? 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 5

EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 11/30/2020 2: 24 PM 10.

EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 6

EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 11/30/2020 2: 24 PM 10.

EXAMPLE 1 Evaluate 43/2 in radical form and simplify. 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 7

EXAMPLE 2 Evaluate 41/2 in radical form and simplify. 11/30/2020 2: 24 PM 10.

EXAMPLE 2 Evaluate 41/2 in radical form and simplify. 11/30/2020 2: 24 PM 10. 2 - Rational Exponents 8

YOUR TURN Evaluate (– 27)2/3 in radical form and simplify. 11/30/2020 2: 25 PM

YOUR TURN Evaluate (– 27)2/3 in radical form and simplify. 11/30/2020 2: 25 PM 10. 2 - Rational Exponents 9

EXAMPLE 3 Evaluate – 274/3 in radical form and Use calculator simplify. to check

EXAMPLE 3 Evaluate – 274/3 in radical form and Use calculator simplify. to check Hint: Remember, the negative is OUTSIDE of the base 10 11/30/2020 2: 25 PM 10. 2 - Rational Exponents

EXAMPLE 4 Evaluate in radical form and simplify. 11 11/30/2020 2: 25 PM 10.

EXAMPLE 4 Evaluate in radical form and simplify. 11 11/30/2020 2: 25 PM 10. 2 - Rational Exponents

NTH ROOT RULE • M is the power (exponent) • N is the root

NTH ROOT RULE • M is the power (exponent) • N is the root • A is the base DROP AND SWAP 11/30/2020 2: 25 PM 10. 2 - Rational Exponents 12

EXAMPLE 5 Evaluate (27)– 2/3 in radical form and simplify. 11/30/2020 2: 25 PM

EXAMPLE 5 Evaluate (27)– 2/3 in radical form and simplify. 11/30/2020 2: 25 PM 10. 2 - Rational Exponents 13

EXAMPLE 6 Evaluate (– 64)– 2/3 in radical form and simplify. 11/30/2020 2: 25

EXAMPLE 6 Evaluate (– 64)– 2/3 in radical form and simplify. 11/30/2020 2: 25 PM 10. 2 - Rational Exponents 14

YOUR TURN Evaluate 11/30/2020 2: 25 PM in radical form and simplify. 10. 2

YOUR TURN Evaluate 11/30/2020 2: 25 PM in radical form and simplify. 10. 2 - Rational Exponents 15

PROPERTIES OF EXPONENTS Product of a Power: Power of a Product: Negative Power Property:

PROPERTIES OF EXPONENTS Product of a Power: Power of a Product: Negative Power Property: Quotient Power Property: 11/30/2020 2: 25 PM 10. 2 - Rational Exponents 16

EXAMPLE 7 Simplify • Saying goes: BASE, ADD If the BASES are the same,

EXAMPLE 7 Simplify • Saying goes: BASE, ADD If the BASES are the same, ADD the powers 11/30/2020 2: 25 PM 10. 2 - Rational Exponents 17

EXAMPLE 8 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 18

EXAMPLE 8 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 18

YOUR TURN Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 19

YOUR TURN Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 19

EXAMPLE 9 Simplify • Saying goes: POWER, MULTIPLY If the POWERS are near each

EXAMPLE 9 Simplify • Saying goes: POWER, MULTIPLY If the POWERS are near each other, MULTIPLY the powers – usually deals with PARENTHESES 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 20

EXAMPLE 10 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 21

EXAMPLE 10 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 21

YOUR TURN Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 22

YOUR TURN Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 22

EXAMPLE 11 Simplify • Saying goes: When dividing an expression with a power, SUBTRACT

EXAMPLE 11 Simplify • Saying goes: When dividing an expression with a power, SUBTRACT the powers. 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 23

EXAMPLE 12 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 24

EXAMPLE 12 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 24

EXAMPLE 13 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 25

EXAMPLE 13 Simplify 11/30/2020 2: 26 PM 10. 2 - Rational Exponents 25

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You simplified rational expressions Solve rational equations rationalYou simplified rational expressions Solve rational equations rational
SWBATsimplify radicals using the product property of radicalsSWBATsimplify radicals using the product property of radicals
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Simplify Radicals 1 Lesson objective to simplify radicalsSimplify Radicals 1 Lesson objective to simplify radicals
SWBATsimplify radicals using the product property of radicalsSWBATsimplify radicals using the product property of radicals
Equations with Radicals Kathy Lydens Equations with RadicalsEquations with Radicals Kathy Lydens Equations with Radicals
3 3 Simplifying Radicals Objectives To simplify radicals3 3 Simplifying Radicals Objectives To simplify radicals
Roots and Radicals Roots and Radicals also calledRoots and Radicals Roots and Radicals also called