\( \begin{array}{l}11 \text { Permudahkan/Simplify } 3^{4} \times 3^{n^{1}} \times 27^{2+n} \\ \text { A } 3^{2 n+10} \\ \text { B } 3^{4 n+10} \\ \text { C } 3^{5 n+8} \\ \text { D } 3^{3 n+10}\end{array} \quad 3^{4} \times 3^{n} \times\left(3^{3}\right)^{\frac{2}{2}} \)

To simplify the expression \(3^4 \times 3^n \times 27^{2+n}\), we start by rewriting \(27\) as \(3^3\). Thus, \(27^{2+n} = (3^3)^{2+n} = 3^{3(2+n)} = 3^{6 + 3n}\). Now we can consolidate everything: \[ 3^{4} \times 3^{n} \times 3^{6 + 3n} \] Using the properties of exponents, we can add the exponents together: \[ = 3^{4 + n + 6 + 3n} = 3^{10 + 4n} \] Comparing with the answer options, none of them match this exact form. However, if there was an oversight in interpreting the exponent rules or rewriting, always revisit each exponent addition step, especially when applying rules like \(a^m \times a^n = a^{m+n}\). Now, let's break down how we can tackle problems like these to ensure we don't miss any detail! Consistency is key in math; when simplifying things, always observe how the exponent rules apply to your bases, especially with products of powers. A common mistake is to miscalculate or overlook smaller components, like associating powers improperly. Double-checking your work can save you from unclear results! Keep practicing with similar problems to strengthen your understanding of exponent rules and manipulations! This will ensure you're confident when facing diverse questions in the future.