Question
\( \sqrt[ 3 ] { 27 x ^ { 9 } y ^ { 12 } } \quad [ 3 ] \)
Ask by Collins Norris. in South Africa
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified form is \( 3x^3y^4 \).
Solution
Calculate or simplify the expression \( \sqrt[3]{27x^9y^{12}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\sqrt[3]{27x^{9}y^{12}}\)
- step1: Transform the expression:
\(\sqrt[3]{\left(3x^{3}y^{4}\right)^{3}}\)
- step2: Simplify the root:
\(3x^{3}y^{4}\)
The simplified form of \( \sqrt[3]{27x^9y^{12}} \) is \( 3x^3y^4 \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To simplify \( \sqrt[3]{27x^9y^{12}} \), we notice that \( 27 = 3^3 \). So, we can express it as \( \sqrt[3]{3^3 \cdot x^9 \cdot y^{12}} \). By applying the property \( \sqrt[3]{a^3} = a \), we get \( 3 \cdot x^{9/3} \cdot y^{12/3} = 3 \cdot x^3 \cdot y^4 \). This results in \( 3x^3y^4 \). Now you know how to extract cubed roots and simplify expressions! If you find polynomial roots interesting, consider exploring how various root extrication techniques apply to other equations in algebra. Delving deeper into algebraic identities can uncover patterns that lead to even quicker solutions to more complex problems!
