\( \left. \begin{array} { l l } { 1 } & { 3 ^ { 2 } \times 3 ^ { 3 } } \\ { 2 } & { 2 ^ { 4 } \times 4 \times 8 } \\ { 3 } & { ( 2 x ^ { 5 } y ^ { 2 } ) ( 7 x ^ { 3 } y ^ { 4 } ) ( - 5 x ^ { 2 } y ) } \end{array} \right. \)

First, let's break down those expressions! For the first row, \(3^2 \times 3^3\) can be simplified using the property of exponents, yielding \(3^{2+3} = 3^5 = 243\). In the second row, \(2^4\) equals 16, and then we have \(4 = 2^2\) and \(8 = 2^3\). So, we can multiply these together: \(16 \times 2^2 \times 2^3 = 16 \times 2^{2+3} = 16 \times 2^5 = 16 \times 32 = 512\). Now, for the last row, we multiply the coefficients and add the exponents for \(x\) and \(y\). The coefficient calculation results in \(2 \times 7 \times (-5) = -70\) and the exponents of \(x\) and \(y\) add up to \(5 + 3 + 2\) and \(2 + 4 + 1\) respectively. This yields \(x^{10}\) and \(y^{7}\). Thus, the simplified expression is \(-70 x^{10} y^{7}\).