To solve the given expression, we need to break it down step by step. The expression is:

\[ \sqrt{\frac{4}{5}} + \sqrt{\frac{26}{4}} + \sqrt{\frac{26}{4}} \sqrt{\frac{81}{100}} \sqrt{\frac{9}{16}} \sqrt{\frac{4}{5}} + \sqrt{\frac{26}{4}} + \sqrt{\frac{26}{4}} \sqrt{\frac{81}{100}} \sqrt{\frac{9}{16}} \]

First, let's simplify each square root term individually:

1. \( \sqrt{\frac{4}{5}} \):
\[ \sqrt{\frac{4}{5}} = \frac{\sqrt{4}}{\sqrt{5}} = \frac{2}{\sqrt{5}} \]

2. \( \sqrt{\frac{26}{4}} \):
\[ \sqrt{\frac{26}{4}} = \frac{\sqrt{26}}{\sqrt{4}} = \frac{\sqrt{26}}{2} \]

3. \( \sqrt{\frac{81}{100}} \):
\[ \sqrt{\frac{81}{100}} = \frac{\sqrt{81}}{\sqrt{100}} = \frac{9}{10} \]

4. \( \sqrt{\frac{9}{16}} \):
\[ \sqrt{\frac{9}{16}} = \frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4} \]

Now, substitute these simplified forms back into the expression:

\[ \frac{2}{\sqrt{5}} + \frac{\sqrt{26}}{2} + \frac{\sqrt{26}}{2} \cdot \frac{9}{10} \cdot \frac{3}{4} \cdot \frac{2}{\sqrt{5}} + \frac{\sqrt{26}}{2} + \frac{\sqrt{26}}{2} \cdot \frac{9}{10} \cdot \frac{3}{4} \]

Next, simplify the product terms:

\[ \frac{\sqrt{26}}{2} \cdot \frac{9}{10} \cdot \frac{3}{4} \cdot \frac{2}{\sqrt{5}} \]

Combine the constants and the square roots:

\[ \frac{\sqrt{26}}{2} \cdot \frac{9 \cdot 3 \cdot 2}{10 \cdot 4 \cdot \sqrt{5}} = \frac{\sqrt{26}}{2} \cdot \frac{54}{40 \sqrt{5}} = \frac{\sqrt{26}}{2} \cdot \frac{27}{20 \sqrt{5}} = \frac{27 \sqrt{26}}{40 \sqrt{5}} \]

Now, the entire expression becomes:

\[ \frac{2}{\sqrt{5}} + \frac{\sqrt{26}}{2} + \frac{27 \sqrt{26}}{40 \sqrt{5}} + \frac{2}{\sqrt{5}} + \frac{\sqrt{26}}{2} + \frac{27 \sqrt{26}}{40 \sqrt{5}} \]

Combine like terms:

\[ 2 \cdot \frac{2}{\sqrt{5}} + 2 \cdot \frac{\sqrt{26}}{2} + 2 \cdot \frac{27 \sqrt{26}}{40 \sqrt{5}} \]

Simplify further:

\[ \frac{4}{\sqrt{5}} + \sqrt{26} + \frac{54 \sqrt{26}}{40 \sqrt{5}} \]

\[ \frac{4}{\sqrt{5}} + \sqrt{26} + \frac{27 \sqrt{26}}{20 \sqrt{5}} \]

This is the simplified form of the given expression.