Algebra 2 6-4 Guided Practice: Rational Exponents

Last updated over 3 years ago

34 questions

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Library

Algebra 2 6-4 Guided Practice: Rational Exponents

Last updated over 3 years ago

34 questions

3

10

Solve It! On the canvas, show how to cut the three linked 1-squares into congruent pieces, each with size ¾.

A.APR.7

3

10

Take Note: Write the expression below in exponent form.

10

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10

Problem 2 Got It? Reasoning: Refer to the definition of rational exponent.

Explain the need for the restriction that a ≠ 0 if m is negative.
(In other words, if m is negative, why can't a be zero?)
HINT: Can a fraction have a denominator that is equal to 0?

A.APR.7

N.RN.1

3

8

Draggable item		Corresponding Item

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N.RN.2

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N.RN.2

Take Note: Take a moment to add the properties of rational exponents to your notes.

12

Draggable item		Corresponding Item

10

Take Note: Describe the process of simplifying radical expressions.
How do you know if you can simplify the expression in the first place?
What are the 2 steps for simplifying the expression?

10

N.RN.2

10

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10

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3

10

Take Note: How are methods 1 and 2 different in Problem 5A?

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5

Take Note: Fill in the blank.

To write an expression with rational exponents in simplest form, write every exponent as a _______ number.

10

N.RN.2

10

N.RN.2

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

10

Solve It! On the canvas, show how to cut the three linked 1-squares into congruent pieces, each with size ¾.

A.APR.7

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

10

Take Note: Write the expression below in exponent form.

10

Take Note: Write the expression below in radical form.

10

Take Note: Define principal root.

10

N.RN.2

10

N.RN.2

10

N.RN.2

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 2 Got It? What is the expression in radical form?

Problem 2 Got It? What is the expression in exponential form?

Problem 2 Got It? Reasoning: Refer to the definition of rational exponent.

Explain the need for the restriction that a ≠ 0 if m is negative.
(In other words, if m is negative, why can't a be zero?)
HINT: Can a fraction have a denominator that is equal to 0?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use the properties of rational exponents to match equivalent expressions below.

Draggable item		Corresponding Item
x^{\frac{3}{2}}		\sqrt[3]{2}
\sqrt[c]{b^{a}}		(2^{3})^{\frac{1}{2}}
x^{\frac{2}{3}}		b^{\frac{c}{a}}
\sqrt[a]{b^{c}}		(\sqrt[c]{b})^a

10

N.RN.2

10

N.RN.2

Take Note: Take a moment to add the properties of rational exponents to your notes.

Take Note: Use the properties of rational exponents to match equivalent expressions.

Draggable item		Corresponding Item
b^{-x}		x^{a+b}
(\frac{a}{b})^{x}		\frac{1}{b^{x}}
(ab)^{x}		x^{a \cdot b}
(x^{a})^b		a^{x-y}
x^{a}\cdot x^{b}		a^{x}b^{x}
\frac{a^{x}}{a^{y}}		\frac{a^{x}}{b^{x}}

10

Take Note: Describe the process of simplifying radical expressions.
How do you know if you can simplify the expression in the first place?
What are the 2 steps for simplifying the expression?

10

N.RN.2

10

N.RN.2

10

N.RN.2

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: How are methods 1 and 2 different in Problem 5A?

10

N.RN.2

10

N.RN.2

10

N.RN.2

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

5

Take Note: Fill in the blank.

To write an expression with rational exponents in simplest form, write every exponent as a _______ number.

10

N.RN.2

10

N.RN.2

10

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Write the expression below in radical form.

Take Note: Define principal root.

Problem 1 Got It?

A

B

C

D

Problem 1 Got It?

A

B

C

D

Problem 1 Got It?

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 2 Got It? What is the expression in radical form? 

Problem 2 Got It? What is the expression in radical form? 

Problem 2 Got It? What is the expression in exponential form? 

Problem 2 Got It? What is the expression in exponential form? 

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Take Note: Use the properties of rational exponents to match equivalent expressions below.

x^{\frac{3}{2}}

\sqrt[3]{2}

\sqrt[c]{b^{a}}

(2^{3})^{\frac{1}{2}}

x^{\frac{2}{3}}

b^{\frac{c}{a}}

\sqrt[a]{b^{c}}

(\sqrt[c]{b})^a

Problem 3 Got It? Planetary Motion: Use the function
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Venusian year if Venus is 0.72 AU from the sun?

A

B

C

D

Problem 3 Got It? Planetary Motion: Use the function
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Jovian year if Jupiter is 5.46 AU from the sun?

A

B

C

D

Take Note: Use the properties of rational exponents to match equivalent expressions.

b^{-x}

x^{a+b}

(\frac{a}{b})^{x}

\frac{1}{b^{x}}

(ab)^{x}

x^{a \cdot b}

(x^{a})^b

a^{x-y}

x^{a}\cdot x^{b}

a^{x}b^{x}

\frac{a^{x}}{a^{y}}

\frac{a^{x}}{b^{x}}

Problem 4 Got It?

A

B

C

D

Problem 4 Got It?

A

B

C

D

Problem 4 Got It?

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 5 Got It?

A

B

C

D

Problem 5 Got It?

A

B

C

D

Problem 5 Got It?

A

B

C

D

Video Check: Select all that apply with regards to the video embedded directly above this item.

🕵️ I carefully watched the entire video.

📵 I removed distractions from my field of view while watching the entire video.

🎧 I used headphones (or earbuds) to listen to the entire video as I watched it.

✋ I sought clarification, as needed, to understand each concept in the video.

🎓 I understand each concept in the video and feel ready to move on.

🎯 I feel prepared to complete challenging problems related to the video.

❌ None of these statements apply.

Problem 6 Got It?

A

B

C

D

Problem 6 Got It?

A

B

C

D

Problem 1 Got It?

A

B

C

D

Problem 1 Got It?

A

B

C

D

Problem 1 Got It?

A

B

C

D

Problem 3 Got It? Planetary Motion: Use the function 
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Venusian year if Venus is 0.72 AU from the sun?

A

B

C

D

Problem 3 Got It? Planetary Motion: Use the function 
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Jovian year if Jupiter is 5.46 AU from the sun?

A

B

C

D

Problem 4 Got It?

A

B

C

D

Problem 4 Got It?

A

B

C

D

Problem 4 Got It?

A

B

C

D

Problem 5 Got It?

A

B

C

D

Problem 5 Got It?

A

B

C

D

Problem 5 Got It?

A

B

C

D

Problem 6 Got It?

A

B

C

D

Problem 6 Got It?

A

B

C

D

Algebra 2 6-4 Guided Practice: Rational Exponents

Algebra 2 6-4 Guided Practice: Rational Exponents

Solve It! On the canvas, show how to cut the three linked 1-squares into congruent pieces, each with size ¾.

Take Note: Write the expression below in exponent form.

Problem 2 Got It? Reasoning: Refer to the definition of rational exponent. Explain the need for the restriction that a ≠ 0 if m is negative. (In other words, if m is negative, why can't a be zero?) HINT: Can a fraction have a denominator that is equal to 0?

Take Note: Describe the process of simplifying radical expressions. How do you know if you can simplify the expression in the first place?What are the 2 steps for simplifying the expression?

Take Note: How are methods 1 and 2 different in Problem 5A?

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Solve It! On the canvas, show how to cut the three linked 1-squares into congruent pieces, each with size ¾.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Write the expression below in exponent form.

Take Note: Write the expression below in radical form.

Take Note: Define principal root.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Problem 2 Got It? What is the expression in radical form?

Problem 2 Got It? What is the expression in radical form?

Problem 2 Got It? What is the expression in exponential form?

Problem 2 Got It? What is the expression in exponential form?

Problem 2 Got It? Reasoning: Refer to the definition of rational exponent. Explain the need for the restriction that a ≠ 0 if m is negative. (In other words, if m is negative, why can't a be zero?) HINT: Can a fraction have a denominator that is equal to 0?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Use the properties of rational exponents to match equivalent expressions below.

Take Note: Use the properties of rational exponents to match equivalent expressions.

Take Note: Describe the process of simplifying radical expressions. How do you know if you can simplify the expression in the first place?What are the 2 steps for simplifying the expression?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: How are methods 1 and 2 different in Problem 5A?

Video Check: Select all that apply with regards to the video embedded directly above this item.

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Write the expression below in radical form.

Take Note: Define principal root.

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

Problem 3 Got It? Planetary Motion: Use the function where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Venusian year if Venus is 0.72 AU from the sun?

Problem 3 Got It? Planetary Motion: Use the function where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Jovian year if Jupiter is 5.46 AU from the sun?

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

Problem 5 Got It?

Problem 5 Got It?

Problem 5 Got It?

Problem 6 Got It?

Problem 6 Got It?

Problem 2 Got It? Reasoning: Refer to the definition of rational exponent.

Explain the need for the restriction that a ≠ 0 if m is negative.
(In other words, if m is negative, why can't a be zero?)
HINT: Can a fraction have a denominator that is equal to 0?

Take Note: Describe the process of simplifying radical expressions.
How do you know if you can simplify the expression in the first place?
What are the 2 steps for simplifying the expression?

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Problem 2 Got It? Reasoning: Refer to the definition of rational exponent.

Explain the need for the restriction that a ≠ 0 if m is negative.
(In other words, if m is negative, why can't a be zero?)
HINT: Can a fraction have a denominator that is equal to 0?

Take Note: Describe the process of simplifying radical expressions.
How do you know if you can simplify the expression in the first place?
What are the 2 steps for simplifying the expression?

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Problem 3 Got It? Planetary Motion: Use the function
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Venusian year if Venus is 0.72 AU from the sun?

Problem 3 Got It? Planetary Motion: Use the function
where d is the distance from the planet to the sun in astronomical units (1 AU is about 93,000,000 miles, or the distance from Earth to the sun). About how many Earth years is a Jovian year if Jupiter is 5.46 AU from the sun?