Answer:
[tex] \sf \: Option \: A \: \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8x \sqrt[6]{ {x}}[/tex]
Step-by-step explanation:
[tex] \sf \: if \: x > 0 \\ \sf \: 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 2 \sqrt[3]{ {x}^{2} } \cdot \: 4 \sqrt{x} \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{2}{3} } \cdot \: {x}^{ \frac{1}{2} } \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} =8 {x}^{ \frac{2}{3} + \frac{1}{2} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{4 + 3}{3 \times 2} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 {x}^{ \frac{7}{6} } \\ \sf 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 \sqrt[6]{ {x}^{7} } \\ \sf\ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8 \sqrt[6]{ {x}^{6} + x } \\ \sf \ 2 \sqrt[3]{ {x}^{2} } \cdot \: \sqrt{16x} = 8x \sqrt[6]{ {x}}[/tex]
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