\( \sqrt[ 3 ] { 27 x ^ { 9 } y ^ { 12 } } \quad [ 3 ] \)

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!