8. To extract roots from the radical √ab¹², Jenna wrote the following: √ab¹² = √a· √b¹² 12 = √(a³)² √(bº)² = |a³| b a. Is Jenna's work correct? If not, show how you would correct it. (N.RN.A.2) b. Explain why Jenna used the absolute value symbol around a but not around be. (N.RN.A.2)
8. To extract roots from the radical √ab¹², Jenna wrote the following: √ab¹² = √a· √b¹² 12 = √(a³)² √(bº)² = |a³| b a. Is Jenna's work correct? If not, show how you would correct it. (N.RN.A.2) b. Explain why Jenna used the absolute value symbol around a but not around be. (N.RN.A.2)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Radical Expressions and Functions
#### 1. Simplify the Expression
\[
\sqrt[3]{-8r} + \sqrt[3]{125r} - \sqrt[3]{-1000r}
\]
---
#### 2. Extracting Roots from Radicals
To extract roots from the radical \(\sqrt[3]{a^2 b^{12}}\), Jenna wrote the following:
\[
\sqrt[3]{a^2 b^{12}} = \sqrt[3]{a^2} \cdot \sqrt[3]{b^{12}}
\]
\[
= (\sqrt[3]{a^2})^k \cdot (\sqrt[3]{b^{12}})^k
\]
\[
= |a|\cdot |b2|
\]
* **Is Jenna's work correct? If not, show how you would correct it. (N.RN.A.2)**
* **Explain why Jenna used the absolute value symbol around \(a^2\) but not around \(b^2\). (N.RN.A.2)**
---
#### 3. Equivalent Expressions in Radical Form
Write an equivalent expression in radical form for each expression. (N.RN.A.2)
---
#### 4. Function Transformation
Describes the transformation \( f(x) = \log(x + 2) - 3 \). (F.IF.B.4)
---
#### 5. Compound Interest Problem
A deposit of $4000 is made into a savings account that pays 3.18% annual interest rate compounded quarterly.
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \(A = \text{amount in account}\)
- \(P = \text{principal invested}\)
- \(r = \text{annual interest rate}\)
- \(n = \text{number of times per year that interest is compounded}\)
- \(t = \text{number of years}\)
* **How much money will be in the account after four years? (F.IF.A.2)**
---
#### 6. Exponential Function
Consider the function \(f(x) = 2^x\):
* **Complete the following table of values for this function. (F.IF.A.2)**](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe78f7d0f-626d-4ef1-bc58-30bf6b75a3d5%2F9aac2a0b-1b16-4907-92e8-4eef0b0a66cd%2Fqu74oh1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Radical Expressions and Functions
#### 1. Simplify the Expression
\[
\sqrt[3]{-8r} + \sqrt[3]{125r} - \sqrt[3]{-1000r}
\]
---
#### 2. Extracting Roots from Radicals
To extract roots from the radical \(\sqrt[3]{a^2 b^{12}}\), Jenna wrote the following:
\[
\sqrt[3]{a^2 b^{12}} = \sqrt[3]{a^2} \cdot \sqrt[3]{b^{12}}
\]
\[
= (\sqrt[3]{a^2})^k \cdot (\sqrt[3]{b^{12}})^k
\]
\[
= |a|\cdot |b2|
\]
* **Is Jenna's work correct? If not, show how you would correct it. (N.RN.A.2)**
* **Explain why Jenna used the absolute value symbol around \(a^2\) but not around \(b^2\). (N.RN.A.2)**
---
#### 3. Equivalent Expressions in Radical Form
Write an equivalent expression in radical form for each expression. (N.RN.A.2)
---
#### 4. Function Transformation
Describes the transformation \( f(x) = \log(x + 2) - 3 \). (F.IF.B.4)
---
#### 5. Compound Interest Problem
A deposit of $4000 is made into a savings account that pays 3.18% annual interest rate compounded quarterly.
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- \(A = \text{amount in account}\)
- \(P = \text{principal invested}\)
- \(r = \text{annual interest rate}\)
- \(n = \text{number of times per year that interest is compounded}\)
- \(t = \text{number of years}\)
* **How much money will be in the account after four years? (F.IF.A.2)**
---
#### 6. Exponential Function
Consider the function \(f(x) = 2^x\):
* **Complete the following table of values for this function. (F.IF.A.2)**
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