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Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
![**Evaluate \( 8^{\frac{5}{3}} \)**
This expression involves calculating the power of 8 raised to the fraction \(\frac{5}{3}\). First, recognize that \( 8^{\frac{5}{3}} \) can be broken down into \((8^{\frac{1}{3}})^5\).
Steps to Solve:
1. **Find the cube root of 8**:
\[
8^{\frac{1}{3}} = 2
\]
because \(2^3 = 8\).
2. **Raise the result to the 5th power**:
\[
(2)^5 = 32
\]
Thus, the evaluation of \( 8^{\frac{5}{3}} \) is 32.](https://content.bartleby.com/qna-images/question/85442580-55b3-46cc-9a23-66f350670659/4d6f5b67-f369-452b-9660-82dd83abcf91/nubvk1g_thumbnail.png)
Transcribed Image Text:**Evaluate \( 8^{\frac{5}{3}} \)**
This expression involves calculating the power of 8 raised to the fraction \(\frac{5}{3}\). First, recognize that \( 8^{\frac{5}{3}} \) can be broken down into \((8^{\frac{1}{3}})^5\).
Steps to Solve:
1. **Find the cube root of 8**:
\[
8^{\frac{1}{3}} = 2
\]
because \(2^3 = 8\).
2. **Raise the result to the 5th power**:
\[
(2)^5 = 32
\]
Thus, the evaluation of \( 8^{\frac{5}{3}} \) is 32.
Expert Solution
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Step 1
Power: - A mathematical formula that can be used to specify exactly how many times a number should be utilized in a multiplication procedure is known as power. It is an expression that explains repeated multiplication of the same supplied integer in simple terms. “Raising a number to the power of any other number” is how power is expressed in mathematics.
Law of power of power: -
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