Let $P(x) = 0$ be the polynomial equation of least possible degree, with rational coefficients, having $\sqrt[3]{7} + \sqrt[3]{49}$ as a root.  Compute the product of all of the roots of $P(x) = 0.$
Question:
Let $P(x) = 0$ be the polynomial equation of least possible degree, with rational coefficients, having $\sqrt[3]{7} + \sqrt[3]{49}$ as a root.  Compute the product of all of the roots of $P(x) = 0.$
Answer:
Let's think step by step.

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Let $P(x) = 0$ be the polynomial equation of least possible degree, with rational coefficients, having $\sqrt[3]{7} + \sqrt[3]{49}$ as a root.  Compute the product of all of the roots of $P(x) = 0.$
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