[tex]\mathbf{Task.} ~ \mathrm{Rewrite~the~expression~in~the~form~} k \cdot x^{n}.[/tex]
[tex]First~way\colon[/tex]
[tex]\left(16\sqrt{x^{3}} \right)^{\tfrac{1}{4} }= \left(2^{4}\cdot x^{\tfrac{3}{2} } \right)^\bigg{\frac{1}{4} } = 2^{4 \cdot \tfrac{1}{4} } \cdot x^{\tfrac{3}{2} \cdot \tfrac{1}{4} } = 2 \cdot x^{\tfrac{3}{8} }[/tex]
[tex]Second~way\colon[/tex]
[tex]\left(16\sqrt{x^{3}} \right)^{\tfrac{1}{4} }= \sqrt[4]{16 \cdot \sqrt{x^{3}}} = \sqrt[4]{2^{4}} \cdot \sqrt[4]{\sqrt{x^{3}}} = 2 \cdot \sqrt[8]{x^{3}} = 2 \cdot x^{\tfrac{3}{8} }[/tex]
[tex]Answer\colon~2 \cdot x^{\tfrac{3}{8} }. ~ \blacktriangle[/tex]
