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Completion requirements
Write the mixed radical \(5t\sqrt[{4}]{2}\) as an entire radical.
\(\begin{align}
5t\sqrt[4]{2} &= \sqrt[4]{{\left({5t} \right)^4}}\cdot \sqrt[4]{2} \\
&= \sqrt[4]{{5^4\cdot t^4\cdot 2}} \\
&= \sqrt[4]{{1\thinspace 250t^4}} \\
\end{align}\)
5t\sqrt[4]{2} &= \sqrt[4]{{\left({5t} \right)^4}}\cdot \sqrt[4]{2} \\
&= \sqrt[4]{{5^4\cdot t^4\cdot 2}} \\
&= \sqrt[4]{{1\thinspace 250t^4}} \\
\end{align}\)