Algebra 2 6-4 Guided Practice: Rational Exponents

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

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

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

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Take Note: Write the expression below in exponent form.

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Take Note: Write the expression below in radical form.

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Take Note: Define principal root.

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Problem 1 Got It?

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Problem 1 Got It?

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Problem 1 Got It?

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

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

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

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

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

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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?

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

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

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

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

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

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

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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?

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Problem 4 Got It?

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Problem 4 Got It?

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Problem 4 Got It?

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

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

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Problem 5 Got It?

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Problem 5 Got It?

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Problem 5 Got It?

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

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Take Note: Fill in the blank.

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

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Problem 6 Got It?

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Problem 6 Got It?

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Algebra 2 6-4 Guided Practice: Rational Exponents

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.

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

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?

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

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?

Problem 5 Got It?

Problem 5 Got It?

Problem 5 Got It?

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

Problem 6 Got It?

Problem 6 Got It?

🧠 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.

Problem 1 Got It?

Problem 1 Got It?

Problem 1 Got It?

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.

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?

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?

Problem 4 Got It?

Problem 4 Got It?

Problem 4 Got It?

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?

Problem 5 Got It?

Problem 5 Got It?

Problem 5 Got It?

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

Problem 6 Got It?

Problem 6 Got It?

🧠 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?

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?

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?

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?