Simplify and write your answers in exponential form: 2.1.1 \( \begin{array}{ll}\text { 2.1.2 } & \left(3^{3}\right)^{2} \\ \text { 2.1.3 } & \left(3.4^{3}\right)^{2} \\ \text { 2.1.4 } & \left(\frac{\left.3.5^{2}\right)^{2} \times\left(4.5^{4}\right)^{2}}{2}\right)^{2}\end{array} \)

Let's simplify each expression step by step: **2.1.2** \((3^{3})^{2} = 3^{3 \times 2} = 3^{6}\) **2.1.3** \((3.4^{3})^{2} = 3^{2} \cdot (4^{3})^{2} = 3^{2} \cdot 4^{3 \times 2} = 3^{2} \cdot 4^{6}\) **2.1.4** \(\left(\frac{(3.5^{2})^{2} \times (4.5^{4})^{2}}{2}\right)^{2}\) First, simplify the numerator: \((3 \cdot 5^{2})^{2} = 3^{2} \cdot (5^{2})^{2} = 3^{2} \cdot 5^{4}\) \((4 \cdot 5^{4})^{2} = 4^{2} \cdot (5^{4})^{2} = 4^{2} \cdot 5^{8}\) Now, multiplying those: \( (3^{2} \cdot 5^{4}) \times (4^{2} \cdot 5^{8}) = 3^{2} \cdot 4^{2} \cdot 5^{(4 + 8)} = 3^{2} \cdot 4^{2} \cdot 5^{12}\) Now, divide by 2: \(\frac{3^{2} \cdot 4^{2} \cdot 5^{12}}{2} = \frac{3^{2} \cdot (2^{2}) \cdot 5^{12}}{2} = 3^{2} \cdot 2^{2-1} \cdot 5^{12} = 3^{2} \cdot 2^{1} \cdot 5^{12}\) Finally, take the square: \(\left(3^{2} \cdot 2^{1} \cdot 5^{12}\right)^{2} = 3^{2 \cdot 2} \cdot 2^{2 \cdot 1} \cdot 5^{2 \cdot 12} = 3^{4} \cdot 2^{2} \cdot 5^{24}\) Thus, the final simplified forms in exponential notation are: **2.1.1:** \(3^{6}\) **2.1.2:** \(3^{2} \cdot 4^{6}\) **2.1.3:** \(3^{4} \cdot 2^{2} \cdot 5^{24}\)