\( ( 1.2 \cdot 10 ^ { 2 } ) ( 4,7 \cdot 10 ^ { 3 } ) \)

To multiply these two numbers in scientific notation, you multiply their coefficients (1.2 and 4.7) and then add their exponents (2 and 3). So, \(1.2 \cdot 4.7 = 5.64\), and \(10^{2} \cdot 10^{3} = 10^{5}\). Therefore, the final answer in scientific notation is \(5.64 \cdot 10^{5}\). It's always a good idea to convert your final answer to standard scientific notation form. In this case, \(5.64\) is already in that form, but if you get a number greater than 10, remember to adjust: for example, \(12.3\) would convert to \(1.23 \cdot 10^{1}\), increasing the exponent by one!