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
![**Exercise: Simplification of Algebraic Expression**
**Task:** Simplify the expression completely:
\[
\frac{(3x^4)^3}{x^{-2}}
\]
**Input Box:** [ ]
**Points Possible:** 1
**Attempt Information:** This is attempt 1 of 4.
**Action Required:** Click the "Submit" button once you have entered your answer.
---
**Explanation:**
To simplify the given expression, follow these steps:
1. Simplify the numerator: \((3x^4)^3\)
- Apply the power of a power rule: \((a^m)^n = a^{m \cdot n}\)
- So, \((3x^4)^3 = 3^3 \cdot (x^4)^3 = 27x^{12}\).
2. Simplify the denominator: \(x^{-2}\)
- \(x^{-2}\) means \(\frac{1}{x^2}\).
3. Combine the simplified numerator and denominator:
- \(\frac{27x^{12}}{x^{-2}} = 27x^{12 - (-2)} = 27x^{12 + 2} = 27x^{14}\).
Make sure to input your answer in the box and click "Submit" once you are done!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff28a37cc-4298-4d07-99eb-8c7a0a3a97b5%2F1d3ee8c0-7675-41c3-8658-9226b50119ac%2Fj1h05lb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Exercise: Simplification of Algebraic Expression**
**Task:** Simplify the expression completely:
\[
\frac{(3x^4)^3}{x^{-2}}
\]
**Input Box:** [ ]
**Points Possible:** 1
**Attempt Information:** This is attempt 1 of 4.
**Action Required:** Click the "Submit" button once you have entered your answer.
---
**Explanation:**
To simplify the given expression, follow these steps:
1. Simplify the numerator: \((3x^4)^3\)
- Apply the power of a power rule: \((a^m)^n = a^{m \cdot n}\)
- So, \((3x^4)^3 = 3^3 \cdot (x^4)^3 = 27x^{12}\).
2. Simplify the denominator: \(x^{-2}\)
- \(x^{-2}\) means \(\frac{1}{x^2}\).
3. Combine the simplified numerator and denominator:
- \(\frac{27x^{12}}{x^{-2}} = 27x^{12 - (-2)} = 27x^{12 + 2} = 27x^{14}\).
Make sure to input your answer in the box and click "Submit" once you are done!
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