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

To evaluate the expression: \[ \frac{4}{7}\left(\frac{1}{4}\right)^{2} \] follow these steps: 1. **Calculate the Exponentiation:** First, evaluate \(\left(\frac{1}{4}\right)^{2}\): \[ \left(\frac{1}{4}\right)^{2} = \frac{1^2}{4^2} = \frac{1}{16} \] 2. **Multiply the Fractions:** Now, multiply \(\frac{4}{7}\) by \(\frac{1}{16}\): \[ \frac{4}{7} \times \frac{1}{16} = \frac{4 \times 1}{7 \times 16} = \frac{4}{112} \] 3. **Simplify the Fraction:** Simplify \(\frac{4}{112}\) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4: \[ \frac{4 \div 4}{112 \div 4} = \frac{1}{28} \] **Final Answer:** \[ \frac{4}{7}\left(\frac{1}{4}\right)^{2} = \frac{1}{28} \]