Which expression is equivalent to $$ 16 s^{\frac{1}{2}} $$ ? $$ 8 \sqrt{s} \frac{4}{s} \frac{4}{\sqrt{s}} $$

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To determine which expression is equivalent to $$ 16 s^{\frac{1}{2}} $$, we will simplify each of the given options: $$ 8 \sqrt{s} $$, $$ \frac{4}{s} $$, and $$ \frac{4}{\sqrt{s}} $$.

1. **Simplifying $$ 8 \sqrt{s} $$**:
   $$
   8 \sqrt{s} = 8 s^{\frac{1}{2}}
   $$
   This is not equivalent to $$ 16 s^{\frac{1}{2}} $$.

2. **Simplifying $$ \frac{4}{s} $$**:
   $$
   \frac{4}{s} = 4 s^{-1}
   $$
   This is not equivalent to $$ 16 s^{\frac{1}{2}} $$.

3. **Simplifying $$ \frac{4}{\sqrt{s}} $$**:
   $$
   \frac{4}{\sqrt{s}} = \frac{4}{s^{\frac{1}{2}}} = 4 s^{-\frac{1}{2}}
   $$
   This is also not equivalent to $$ 16 s^{\frac{1}{2}} $$.

None of the expressions $$ 8 \sqrt{s} $$, $$ \frac{4}{s} $$, or $$ \frac{4}{\sqrt{s}} $$ are equivalent to $$ 16 s^{\frac{1}{2}} $$.

Thus, the answer is that none of the provided expressions are equivalent to $$ 16 s^{\frac{1}{2}} $$.
None of the provided expressions are equivalent to $$ 16 s^{\frac{1}{2}} $$.

Which expression is equivalent to ?

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