Sometimes It’s Squared and Sometimes It’s Cubed

Unit 3 ● Lesson 3 ● Activity 1

Find a solution to each equation.

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1. x² = 25
2. z² = 7
3. y³ = 8
4. w³ = 19
5. q³ = 64

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Warm-up

Exponents That Are Unit Fractions

Unit 3

Lesson 3

Complex Numbers and Rational Exponents

Expressions and Equations

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ALGEBRA 2

Unit 3 ● Lesson 3

I can write square and cube roots as exponents.

Learning

Targets

Algebra 2

To the...Half?

Unit 3 ● Lesson 3 ● Activity 2

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Here is a graph that shows y = 9^x

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Estimate the value of 9^1/2

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

To the Half?

What is the actual value of 9^1/2 ? (Check using a calculator)

How is the solution related to 9?

What is the value of this expression: 9^1/2 · 9^1/2?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Rational Exponents

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Fraction of What, Exactly?

Unit 3 ● Lesson 3 ● Activity 3

Use the exponent rules and your understanding of roots to find the exact value of:

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1. 25^1/2
2. 15^1/2
3. 8^1/3
4. 2^1/3

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Exponents and Radicals

Unit 3 ● Lesson 3 ● Activity 4

Match each exponential expression to an equivalent expression.

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• 7³
• 7²
• 7¹
• 7⁰
• 7^-1
• 7^-2
• 7^-3
• 7^1/2
• 7^-½
• 7^1/3
• 7^-1/3

• 49
• 343
• 7
• 1

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Write It Two Ways

Unit 3 ● Lesson 3 ● Activity 4

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1. Write 5^½ using radicals
2. Write using exponents.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Lesson Synthesis

Cool-down