The problem is to evaluate the expression $(\frac{3}{8} \times \frac{9}{16}) \div \frac{1}{4}$.

1. Problem Description

The problem is to evaluate the expression $(\frac{3}{8} \times \frac{9}{16}) \div \frac{1}{4}$.

2. Solution Steps

First, we perform the multiplication inside the parenthesis.

$\frac{3}{8} \times \frac{9}{16} = \frac{3 \times 9}{8 \times 16} = \frac{27}{128}$

Next, we divide the result by $\frac{1}{4}$. Dividing by a fraction is the same as multiplying by its reciprocal.

The reciprocal of $\frac{1}{4}$ is $\frac{4}{1}$, which is equal to

4.

$\frac{27}{128} \div \frac{1}{4} = \frac{27}{128} \times 4 = \frac{27 \times 4}{128} = \frac{108}{128}$

Finally, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is

4.

$\frac{108}{128} = \frac{108 \div 4}{128 \div 4} = \frac{27}{32}$

3. Final Answer

The final answer is $\frac{27}{32}$.