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

To simplify \( \sqrt[3]{27 x^{9} y^{12}} \), you can break it down term by term. The cube root of 27 is 3, since \( 3^3 = 27 \). For the \( x^{9} \) term, the cube root of \( x^9 \) is \( x^{9/3} = x^{3} \). Lastly, the cube root of \( y^{12} \) is \( y^{12/3} = y^{4} \). Putting it all together, you get \( 3x^{3}y^{4} \). So, the answer is \( 3x^{3}y^{4} \). Feeling confident now? Just remember, breaking down each component and applying the rules of exponents makes simplifying these expressions a breeze!