### Instruction: What is $\left(\frac{6}{7}\right)^2 \cdot \left(\frac{1}{2}\right)^2$?### Response: To simplify this expression, I need to apply the rules of exponents and fractions.
First, I can rewrite the expression as $\left(\frac{6}{7} \cdot \frac{1}{2}\right)^2$ by using the rule that $(a \cdot b)^n = a^n \cdot b^n$.
Next, I can simplify the fraction inside the parentheses by multiplying the numerators and the denominators: $\left(\frac{6}{7} \cdot \frac{1}{2}\right)^2 = \left(\frac{6 \cdot 1}{7 \cdot 2}\right)^2 = \left(\frac{6}{14}\right)^2$.
Then, I can reduce the fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2: $\left(\frac{6}{14}\right)^2 = \left(\frac{3}{7}\right)^2$.
Finally, I can square the fraction by squaring the numerator and the denominator: $\left(\frac{3}{7}\right)^2 = \frac{3^2}{7^2} = \frac{9}{49}$.