Find the cube-roots of 3375 x 512

Prime factors of 3375:

Prime factors of 512:

$\sqrt[3]{3375 \times 512}\\[1em] = \sqrt[3]{3375}\times{\sqrt[3]{512}}\\[1em] = \sqrt[3]{(3 \times 3 \times 3)\times(5 \times 5 \times 5)}\times{\sqrt[3]{(2 \times 2 \times 2)\times (2 \times 2 \times 2) \times (2 \times 2 \times 2)}}\\[1em] = (3 \times 5)\times(2 \times 2 \times 2)\\[1em] = (15)\times(8)\\[1em] = 120$

Hence, $\sqrt[3]{3375 \times 512} = 120$