Find the value of the expression

$\left(64 x^{2}+81 y^{2}+144 x y\right)$

Given:

$x=11$

$y=\frac{4}{3}$

$\Rightarrow(8 x)^{2}+(9 y)^{2}+2(8 x)(9 y)$

$\Rightarrow(8 x+9 y)^{2}$

$\Rightarrow\left(8(11)+9\left(\frac{4}{3}\right)\right)^{2}$

$\Rightarrow(88+12)^{2}$

$\Rightarrow(100)^{2}$

$\Rightarrow 10000$

Therefore, the value of the expression $\left(64 x^{2}+81 y^{2}+144 x y\right)$, when $x=11$ and $y=\frac{4}{3}$, is 10000 .