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5 aluate 83

5 aluate 83

Algebra and Trigonometry (6th Edition)
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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**Evaluate \( 8^{\frac{5}{3}} \).** In this problem, you are tasked with evaluating the expression \( 8^{\frac{5}{3}} \). **Steps to solve:** 1. **Convert the expression**: - The expression \( 8^{\frac{5}{3}} \) can be rewritten as \( (8^{\frac{1}{3}})^5 \). - This approach utilizes the property of exponents that states \( a^{m/n} = (a^{1/n})^m \). 2. **Calculate \( 8^{\frac{1}{3}} \)**: - \( 8^{\frac{1}{3}} \) is the cube root of 8. - Since \( 2^3 = 8 \), it follows that \( 8^{\frac{1}{3}} = 2 \). 3. **Raise the result to the 5th power**: - Now, raise 2 to the power of 5: \( 2^5 \). - Calculate: \( 2^5 = 32 \). **Conclusion**: Therefore, the value of \( 8^{\frac{5}{3}} \) is 32.
Transcribed Image Text:**Evaluate \( 8^{\frac{5}{3}} \).** In this problem, you are tasked with evaluating the expression \( 8^{\frac{5}{3}} \). **Steps to solve:** 1. **Convert the expression**: - The expression \( 8^{\frac{5}{3}} \) can be rewritten as \( (8^{\frac{1}{3}})^5 \). - This approach utilizes the property of exponents that states \( a^{m/n} = (a^{1/n})^m \). 2. **Calculate \( 8^{\frac{1}{3}} \)**: - \( 8^{\frac{1}{3}} \) is the cube root of 8. - Since \( 2^3 = 8 \), it follows that \( 8^{\frac{1}{3}} = 2 \). 3. **Raise the result to the 5th power**: - Now, raise 2 to the power of 5: \( 2^5 \). - Calculate: \( 2^5 = 32 \). **Conclusion**: Therefore, the value of \( 8^{\frac{5}{3}} \) is 32.
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