$-256^2=\left(-256\right)^2$-256^2=\left(-256\right)^2

$256^3=\left(-256\right)^3$256^3=\left(-256\right)^3

$\sqrt{\left(-256\right)^2}=-256$\sqrt{\left(-256\right)^2}=-256

$\sqrt[3]{-256}=-\sqrt[3]{256}$\sqrt[3]{-256}=-\sqrt[3]{256}