3. Use the laws to re-write the following expression as a power of $$ x $$ : $$ x \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}} $$

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To rewrite the expression $$ x \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}} $$ as a power of $$ x $$, we will simplify it step by step.

1. Start with the innermost square root:
   $$
   \sqrt{x} = x^{1/2}
   $$

2. Now, we can rewrite the next square root:
   $$
   \sqrt{x \sqrt{x}} = \sqrt{x \cdot x^{1/2}} = \sqrt{x^{1 + 1/2}} = \sqrt{x^{3/2}} = x^{(3/2) \cdot (1/2)} = x^{3/4}
   $$

3. Next, we simplify the next square root:
   $$
   \sqrt{x \sqrt{x \sqrt{x}}} = \sqrt{x \cdot x^{3/4}} = \sqrt{x^{1 + 3/4}} = \sqrt{x^{7/4}} = x^{(7/4) \cdot (1/2)} = x^{7/8}
   $$

4. Now, we simplify the outermost square root:
   $$
   \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}} = \sqrt{x \cdot x^{7/8}} = \sqrt{x^{1 + 7/8}} = \sqrt{x^{15/8}} = x^{(15/8) \cdot (1/2)} = x^{15/16}
   $$

5. Finally, we combine this with the $$ x $$ in front of the expression:
   $$
   x \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}} = x \cdot x^{15/16} = x^{1 + 15/16} = x^{16/16 + 15/16} = x^{31/16}
   $$

Thus, the expression $$ x \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}} $$ can be rewritten as:
$$
\boxed{x^{31/16}}
$$
The expression $$ x \sqrt{x \sqrt{x \sqrt{x \sqrt{x}}}} $$ can be rewritten as $$ x^{31/16} $$.

Use the laws to re-write the following expression as a power of :

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