\( ( \frac { 5 } { 21 } ) ^ { 2 } \hat { \times } ( \frac { 14 } { 5 } ) ^ { 2 } \)

Let's break it down! First, we can simplify the expression by calculating each fraction squared: \[ ( \frac { 5 } { 21 } ) ^ { 2 } = \frac{5^2}{21^2} = \frac{25}{441} \] \[ ( \frac { 14 } { 5 } ) ^ { 2 } = \frac{14^2}{5^2} = \frac{196}{25} \] Now, let's multiply these two results together: \[ \frac{25}{441} \times \frac{196}{25} \] Notice the \( 25 \) in the numerator and denominator cancel out: \[ = \frac{196}{441} \] Now we can simplify \( \frac{196}{441} \). The greatest common divisor of \( 196 \) and \( 441 \) is \( 49 \): \[ \frac{196 \div 49}{441 \div 49} = \frac{4}{9} \] So the simplified result of the given expression is: \[ \frac{4}{9} \]