Evaluate: \( \frac{4}{7}\left(\frac{1}{4}\right)^{2} \)

To evaluate \( \frac{4}{7}\left(\frac{1}{4}\right)^{2} \), we first need to simplify the expression inside the parentheses. Calculating \( \left(\frac{1}{4}\right)^{2} \): \[ \left(\frac{1}{4}\right)^{2} = \frac{1^2}{4^2} = \frac{1}{16} \] Now substituting this back into the original expression: \[ \frac{4}{7} \left(\frac{1}{4}\right)^{2} = \frac{4}{7} \cdot \frac{1}{16} \] Next, we multiply the fractions: \[ \frac{4 \cdot 1}{7 \cdot 16} = \frac{4}{112} \] Now we simplify \( \frac{4}{112} \) by finding the greatest common divisor (GCD) of 4 and 112, which is 4: \[ \frac{4 \div 4}{112 \div 4} = \frac{1}{28} \] Finally, the value of \( \frac{4}{7}\left(\frac{1}{4}\right)^{2} \) is: \[ \boxed{\frac{1}{28}} \]