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  1. Simplify the radical expression \(\frac{{4\sqrt[3]{{54}}}}{{\sqrt[3]{2}}}\).

    \(\begin{align}
     \frac{{4\sqrt[3]{{54}}}}{{\sqrt[3]{2}}} &= 4\sqrt[3]{{\frac{{54}}{2}}} \\
      &= 4\sqrt[3]{{27}} \\
      &= 4 \cdot 3 \\
      &= 12 \\
     \end{align}\)


  2. Simplify the radical expression \(3\sqrt {5p} \cdot 6\sqrt {15p^3 } \). Identify any restrictions on the variable.

    \( p \ge 0\)

    \(\begin{align}
     3\sqrt {5p} \cdot 6\sqrt {15p^3 } &= \left( {18} \right)\sqrt {\left( {5\cdot 15} \right)\left( {p\cdot p^3 } \right)}  \\
      &= 18\sqrt {75p^4 }  \\
      &= 18\cdot 5\cdot p^2 \sqrt 3  \\
      &= 90p^2 \sqrt 3  \\
     \end{align}\)