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djyliett [7]
2 years ago
10

Which expression is equivalent to

Mathematics
2 answers:
Sergio039 [100]2 years ago
6 0

Answer:

\sf \: Option \:  A  \:  \sf \ 2 \sqrt[3]{ {x}^{2} }  \cdot \:  \sqrt{16x}  = 8x \sqrt[6]{ {x}}

Step-by-step explanation:

\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}}

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masya89 [10]2 years ago
4 0

2\sqrt[3]{x^2}\cdot \sqrt{16x}\\\\=2\sqrt[3]{x^2} \cdot 4\sqrt x\\\\=8x^{\tfrac 23} \cdot x^{\tfrac 12}\\\\=8\cdot x^{\tfrac 23 + \tfrac 12}\\\\=8\cdot x^{\tfrac 76}\\\\=8\sqrt[6]{x^7}\\\\=8\sqrt[6]{x^6 \cdot x}\\\\=8x\sqrt[6]{x}

\text{Hence the answer is A}

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