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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![**Transcription for Educational Website**
### Topic: Converting Exponential Expressions to Radicals
**Problem:**
Write each exponential expression as a radical.
**Example (c):**
\[
(5x^2 + 3y^3)^{\frac{-5}{6}}
\]
**Explanation:**
The expression \( (5x^2 + 3y^3)^{\frac{-5}{6}} \) can be rewritten using radical notation. The fractional exponent \(\frac{-5}{6}\) indicates both a root and a reciprocal due to the negative sign.
1. The denominator (6) of the exponent indicates a sixth root.
2. The numerator (-5) indicates the power to which the expression is raised, and the negative sign denotes taking the reciprocal of the entire expression.
Thus, this expression converts to:
\[
\frac{1}{\sqrt[6]{(5x^2 + 3y^3)^5}}
\]
This represents the reciprocal of the sixth root of \((5x^2 + 3y^3)^5\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc821de77-dd96-450a-a649-62f8f8f38521%2Ff3f5a2d6-3745-4096-942f-4df1d8d1dbe1%2F2h3gntq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
### Topic: Converting Exponential Expressions to Radicals
**Problem:**
Write each exponential expression as a radical.
**Example (c):**
\[
(5x^2 + 3y^3)^{\frac{-5}{6}}
\]
**Explanation:**
The expression \( (5x^2 + 3y^3)^{\frac{-5}{6}} \) can be rewritten using radical notation. The fractional exponent \(\frac{-5}{6}\) indicates both a root and a reciprocal due to the negative sign.
1. The denominator (6) of the exponent indicates a sixth root.
2. The numerator (-5) indicates the power to which the expression is raised, and the negative sign denotes taking the reciprocal of the entire expression.
Thus, this expression converts to:
\[
\frac{1}{\sqrt[6]{(5x^2 + 3y^3)^5}}
\]
This represents the reciprocal of the sixth root of \((5x^2 + 3y^3)^5\).
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