What is the value of ${(256)}^{0.16}\times {(256)}^{0.09}$?

It is given that the mathematical expression is ${\left(256\right)}^{0.16}\times {\left(256\right)}^{0.09}$.

$\begin{array}{c}={\left(256\right)}^{\frac{16}{100}}\times {\left(256\right)}^{\frac{9}{100}}\end{array}$

$={256}^{\left(\frac{16}{100}+\frac{9}{100}\right)}$

$={256}^{\frac{25}{100}}$

$={256}^{\frac{1}{4}}$

$={\left(4^4\right)}^{\frac{1}{4}}$

$=4^{\frac{4}{4}}$

$=4$
Therefore, the correct answer is 4.