**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.

Answered: Evaluate 81

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

**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

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: - ${(a^{m})}^{n} = a^{m n}$