11. What do you obtain when you raise 27 to the 8/3 power ? * 1/3 of (27 to the 8th power)

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 11: What do you obtain when you raise 27 to the 8/3 power?**

Choices:
- ( ) 1/3 of (27 to the 8th power)
- ( ) 72
- ( ) 6561

Explanation:

1. **Understanding the Expression**: Raising 27 to the 8/3 power means finding \((27^{8/3})\).
2. **Steps to Solve**:
   - First, rewrite the base 27 as \(3^3\) (since \(27 = 3^3\)).
   - Now the expression becomes \((3^3)^{8/3}\).
   - Using the property of exponents \((a^{m})^{n} = a^{mn}\), we get:
     \[
     (3^3)^{8/3} = 3^{(3 \times 8/3)} = 3^8.
     \]
   - Calculate \(3^8\):
     \[
     3^8 = 6561.
     \]

Answer: 
- The correct answer is 6561.
Transcribed Image Text:**Question 11: What do you obtain when you raise 27 to the 8/3 power?** Choices: - ( ) 1/3 of (27 to the 8th power) - ( ) 72 - ( ) 6561 Explanation: 1. **Understanding the Expression**: Raising 27 to the 8/3 power means finding \((27^{8/3})\). 2. **Steps to Solve**: - First, rewrite the base 27 as \(3^3\) (since \(27 = 3^3\)). - Now the expression becomes \((3^3)^{8/3}\). - Using the property of exponents \((a^{m})^{n} = a^{mn}\), we get: \[ (3^3)^{8/3} = 3^{(3 \times 8/3)} = 3^8. \] - Calculate \(3^8\): \[ 3^8 = 6561. \] Answer: - The correct answer is 6561.
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