Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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How to Simplify this equation in a simple way not the long way to solve this but a simpler way to solve this.
Below is a transcription and detailed explanation designed for an educational website. --- **Radical Expression Simplification** The given image presents a radical expression with the following terms under the radical sign: \[ \sqrt[4]{16x^{20}y^{8}} \] **Description:** 1. **Radical Symbol (√) with Degree 4:** This indicates that we are taking the fourth root of the expression inside the radical. 2. **Inside the Radical:** - **16** is a constant term. - **\(x^{20}\)** represents the variable \(x\) raised to the 20th power. - **\(y^{8}\)** represents the variable \(y\) raised to the 8th power. **Simplification Steps:** To simplify this fourth root expression, follow these steps: 1. **Simplify the Constant Term:** - The fourth root of 16. \[ \sqrt[4]{16} = \sqrt[4]{2^4} = 2 \] 2. **Simplify the Variable \(x\):** - The fourth root of \(x^{20}\). \[ \sqrt[4]{x^{20}} = x^{20/4} = x^5 \] 3. **Simplify the Variable \(y\):** - The fourth root of \(y^{8}\). \[ \sqrt[4]{y^{8}} = y^{8/4} = y^2 \] **Combining All Simplified Parts:** \[ \sqrt[4]{16x^{20}y^{8}} = 2x^5y^2 \] Thus, the expression simplifies to \( 2x^5y^2 \). **Conclusion:** Understanding how to simplify radical expressions, especially those involving higher-order roots and variables with exponents, is crucial. Follow the steps of breaking down each part of the expression, simplifying constants, and reducing the exponents systematically to achieve the final simplified form. ---
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Transcribed Image Text:Below is a transcription and detailed explanation designed for an educational website. --- **Radical Expression Simplification** The given image presents a radical expression with the following terms under the radical sign: \[ \sqrt[4]{16x^{20}y^{8}} \] **Description:** 1. **Radical Symbol (√) with Degree 4:** This indicates that we are taking the fourth root of the expression inside the radical. 2. **Inside the Radical:** - **16** is a constant term. - **\(x^{20}\)** represents the variable \(x\) raised to the 20th power. - **\(y^{8}\)** represents the variable \(y\) raised to the 8th power. **Simplification Steps:** To simplify this fourth root expression, follow these steps: 1. **Simplify the Constant Term:** - The fourth root of 16. \[ \sqrt[4]{16} = \sqrt[4]{2^4} = 2 \] 2. **Simplify the Variable \(x\):** - The fourth root of \(x^{20}\). \[ \sqrt[4]{x^{20}} = x^{20/4} = x^5 \] 3. **Simplify the Variable \(y\):** - The fourth root of \(y^{8}\). \[ \sqrt[4]{y^{8}} = y^{8/4} = y^2 \] **Combining All Simplified Parts:** \[ \sqrt[4]{16x^{20}y^{8}} = 2x^5y^2 \] Thus, the expression simplifies to \( 2x^5y^2 \). **Conclusion:** Understanding how to simplify radical expressions, especially those involving higher-order roots and variables with exponents, is crucial. Follow the steps of breaking down each part of the expression, simplifying constants, and reducing the exponents systematically to achieve the final simplified form. ---
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