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2. Evaluate each expression 2-3 (주) 8 3 flip 5-² 10 -100 (우)2 = (64

2. Evaluate each expression 2-3 (주) 8 3 flip 5-² 10 -100 (우)2 = (64

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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### Evaluating Expressions with Exponents The worksheet contains several mathematical expressions that involve evaluating exponents. Below is the transcription and explanation of each expression along with the steps needed to solve them. #### Expression 1: \((-2)^3\) 1. **Expression**: \((-2)^3\) 2. **Calculation**: - You multiply -2 by itself three times: \(-2 \times -2 \times -2\). - Result: \(-8\). #### Expression 2: \((-5)^2\) 1. **Expression**: \((-5)^2\) 2. **Calculation**: - Multiplying -5 by itself: \(-5 \times -5\). - Result: \(25\). #### Expression 3: \(\left(\frac{1}{8}\right)^{-2}\) 1. **Expression**: \(\left(\frac{1}{8}\right)^{-2}\) 2. **Calculation**: - Flip the fraction to undo the negative exponent: \(\left(\frac{8}{1}\right)^2\). - Multiply 8 by itself: \(8 \times 8\). - Result: \(64\). #### Expression 4: \(2^{-3}\) 1. **Expression**: \(2^{-3}\) 2. **Steps**: - Start with \( \left(\frac{2}{1}\right)^{-3} \). - Flip the fraction: \( \left(\frac{1}{2}\right)^3 \). - Multiply \(\frac{1}{2}\) by itself three times: \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\). - Result: \(\frac{1}{8}\). #### Expression 5: \(5^{-2}\) 1. **Expression**: \(5^{-2}\) 2. **Steps**: - Convert to fraction: \(\left(\frac{1}{5}\right)^2\). - Multiply \(\frac{1}{5}\) by itself: \(\frac{1}{5} \times \frac{1}{5}\). - Utilize the exponent rule: \( \frac{1}{25} \). This guide helps in understanding the process of using ex
Transcribed Image Text:### Evaluating Expressions with Exponents The worksheet contains several mathematical expressions that involve evaluating exponents. Below is the transcription and explanation of each expression along with the steps needed to solve them. #### Expression 1: \((-2)^3\) 1. **Expression**: \((-2)^3\) 2. **Calculation**: - You multiply -2 by itself three times: \(-2 \times -2 \times -2\). - Result: \(-8\). #### Expression 2: \((-5)^2\) 1. **Expression**: \((-5)^2\) 2. **Calculation**: - Multiplying -5 by itself: \(-5 \times -5\). - Result: \(25\). #### Expression 3: \(\left(\frac{1}{8}\right)^{-2}\) 1. **Expression**: \(\left(\frac{1}{8}\right)^{-2}\) 2. **Calculation**: - Flip the fraction to undo the negative exponent: \(\left(\frac{8}{1}\right)^2\). - Multiply 8 by itself: \(8 \times 8\). - Result: \(64\). #### Expression 4: \(2^{-3}\) 1. **Expression**: \(2^{-3}\) 2. **Steps**: - Start with \( \left(\frac{2}{1}\right)^{-3} \). - Flip the fraction: \( \left(\frac{1}{2}\right)^3 \). - Multiply \(\frac{1}{2}\) by itself three times: \(\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\). - Result: \(\frac{1}{8}\). #### Expression 5: \(5^{-2}\) 1. **Expression**: \(5^{-2}\) 2. **Steps**: - Convert to fraction: \(\left(\frac{1}{5}\right)^2\). - Multiply \(\frac{1}{5}\) by itself: \(\frac{1}{5} \times \frac{1}{5}\). - Utilize the exponent rule: \( \frac{1}{25} \). This guide helps in understanding the process of using ex
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