<s>[INST] Simplify $2 \sqrt[3]{50x^2 z^5} × 3 \sqrt[3]{15 y^3 z}$ Image of problem
As you can see the answer is $30 y z^2 \sqrt[3]{6x^2}$ . I understand mostly everything in the problem, but one thing that I am having confusion on is where the "30" came from in the answer. I tried many ways to find out how the "30" got there.
 [/INST] $$2\,\sqrt[3]{50\,x^2 z^5} \cdot 3\,\sqrt[3]{15\,\color{red}{y^3} z}=$$
$$=2 \cdot 3 \cdot \color{red}{y} \cdot \sqrt[3]{50\,x^2 z^5} \cdot \sqrt[3]{15\,z}=$$
$$=6\,y \cdot \sqrt[3]{(50\,x^2 z^5)(15 z)}=$$
$$=6\,y \cdot \sqrt[3]{750\,x^2 \color{magenta}{z^6}}=$$
$$=6\,y\color{magenta}{z^2} \cdot \sqrt[3]{2 \cdot 3 \cdot \color{blue}{5^3} \cdot x^2}=$$
$$=6 \cdot \color{blue}{5} \cdot yz^2 \cdot \sqrt[3]{2 \cdot 3 \cdot x^2}=$$
$$=30\,yz^2 \sqrt[3]{6\,x^2}.$$
As you see, $30$ is due to $6\cdot\sqrt[3]{5^3}$, emphatized in blue.
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