Simplify 3(4)^4 square root of 4

$3 {(4)}^{4} \sqrt{4}$

Raise $4$ to the power of $4$ .

$3 \cdot 256 \sqrt{4}$

Multiply $3$ by $256$ .

$768 \sqrt{4}$

Rewrite $4$ as $2^{2}$ .

$768 \sqrt{2^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$768 \cdot 2$

Multiply $768$ by $2$ .

$1536$