Question
$$5^{1/3}\cdot25^{1/3} = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 5^{1/3}\cdot25^{1/3} &= 0&& \text{multiply ALL terms by } \color{blue}{ 3 }. \\[1 em]35^{1/3}\cdot25^{1/3} &= 3\cdot0&& \text{cancel out the denominators} \\[1 em]6 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 6 = 0 } $ is FALSE, we conclude that the equation has no solution.
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