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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Question
![**Problem: Solve for \( n \) in the following equation.**
\[ 4^n \cdot 4^9 = 4^{17} \]
**Options:**
- \( \bigcirc \) 8
- \( \bigcirc \) -4
- \( \bigcirc \) -8
- \( \bigcirc \) 4
**Explanation:**
To solve \( 4^n \cdot 4^9 = 4^{17} \), apply the law of exponents, which states that when you multiply two powers with the same base, you add the exponents.
\[ 4^n \cdot 4^9 = 4^{n+9} \]
Set the expression equal to the right side of the equation:
\[ 4^{n+9} = 4^{17} \]
Since the bases are the same, the exponents must be equal:
\[ n + 9 = 17 \]
Solve for \( n \):
\[ n = 17 - 9 \]
\[ n = 8 \]
Therefore, the correct option is \( \bigcirc \) 8.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb30d7fc0-4739-4205-b977-e5697f99a5bd%2F27642c7f-72a4-4867-aa95-27a9e3cb9d27%2Faddxg5_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem: Solve for \( n \) in the following equation.**
\[ 4^n \cdot 4^9 = 4^{17} \]
**Options:**
- \( \bigcirc \) 8
- \( \bigcirc \) -4
- \( \bigcirc \) -8
- \( \bigcirc \) 4
**Explanation:**
To solve \( 4^n \cdot 4^9 = 4^{17} \), apply the law of exponents, which states that when you multiply two powers with the same base, you add the exponents.
\[ 4^n \cdot 4^9 = 4^{n+9} \]
Set the expression equal to the right side of the equation:
\[ 4^{n+9} = 4^{17} \]
Since the bases are the same, the exponents must be equal:
\[ n + 9 = 17 \]
Solve for \( n \):
\[ n = 17 - 9 \]
\[ n = 8 \]
Therefore, the correct option is \( \bigcirc \) 8.
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