Find the cube-roots of -125 x 1000

$\sqrt[3]{-125 \times 1000}\\[1em] = -\sqrt[3]{125}\times{\sqrt[3]{1000}}$

Prime factors of 125:

$\therefore -\sqrt[3]{125}\times{\sqrt[3]{1000}} = -\sqrt[3]{(5 \times 5 \times 5)}\times{\sqrt[3]{(10 \times 10 \times 10)}}\\[1em] = -5\times 10\\[1em] = -50$

Hence, $\sqrt[3]{-125 \times 1000} = -50$