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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**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.
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
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: -(am)n=amn

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