On dividing $256a^2{b}^2{c}^2$ by $64a^2$, we get:

Perform the division operation:
$$\frac{256a^2{b}^2{c}^2}{64a^2}$$
Separate the numerical constants and the algebraic variables:
$$=\left(\frac{256}{64}\right)\times \left(\frac{a^2}{a^2}\right)\times b^2\times c^2$$
$$=4\times 1\times b^2{c}^2$$
$$=4b^2{c}^2$$