First divide the roots of the same degree:

\(\sqrt[4]{48}:\sqrt[4]{3}=\sqrt[4]{\dfrac{48}{3}}=\sqrt[4]{16}=2\).

Now evaluate the power:

\(\left(\dfrac13\right)^{-2}=3^2=9\).

So the whole expression equals:

\(2+9=11\).

Simplify the first fraction:

\(25^5=(5^2)^5=5^{10}\), so

\(\dfrac{5^{11}}{25^5}=\dfrac{5^{11}}{5^{10}}=5\).

Next:

\(\sqrt[3]{\dfrac{27}{8}}=\dfrac{\sqrt[3]{27}}{\sqrt[3]{8}}=\dfrac{3}{2}\).

Therefore,

\(5-\dfrac{3}{2}=\dfrac{10}{2}-\dfrac{3}{2}=\dfrac{7}{2}\).

Combine the roots of the same degree:

\(\sqrt[5]{8}\cdot\sqrt[5]{4}=\sqrt[5]{32}=2\).

Also, \(10^{-1}=\dfrac{1}{10}\).

Then

\(2-\dfrac{1}{10}=\dfrac{20}{10}-\dfrac{1}{10}=\dfrac{19}{10}\).

\(\sqrt[4]{81}=3\), since \(81=3^4\).

Next:

\(8^4=(2^3)^4=2^{12}\), so

\(\dfrac{2^{11}}{8^4}=\dfrac{2^{11}}{2^{12}}=2^{-1}=\dfrac{1}{2}\).

Therefore,

\(3-\dfrac{1}{2}=\dfrac{6}{2}-\dfrac{1}{2}=\dfrac{5}{2}\).

Use the difference of squares formula:

\((\sqrt{11}+\sqrt{3})(\sqrt{11}-\sqrt{3})=11-3=8\).

Then

\(\sqrt[3]{8}=2\).