\( (3\sqrt {2)^{2}} \)

To simplify \( (3\sqrt{2})^{2} \), you start by applying the power of a product rule, which states that \( (ab)^{n} = a^{n}b^{n} \). Here, \( a = 3 \) and \( b = \sqrt{2} \), so: \[ (3\sqrt{2})^{2} = 3^{2} \cdot (\sqrt{2})^{2} = 9 \cdot 2 = 18. \] So, \( (3\sqrt{2})^{2} = 18 \). Now, let’s talk about how this concept applies in geometry! When dealing with measurements in geometry, especially in contexts like calculating the area of shapes with radical expressions, simplifying roots and squared quantities can make your calculations much more manageable and lead to quicker solutions when working with areas or volumes. Additionally, a common mistake people make with exponents is overlooking the order of operations. When squaring a product, it's essential to remember that each factor gets squared—this applies to everything inside the parentheses. Always distribute that exponent carefully and avoid confusion!