If `a ,\ b ,\ c` are positive real numbers, then `sqrt(a^(-1)b)\ xx\ sqrt(b^(-1)\ c)\ xx\ sqrt(c^(-1)a)` is equal to: `(a)\ 1` (b) `a b c` (c) `sqrt(a b c)` (d) `1/(a b c)`

Explanation

To solve the expression \( \sqrt{a^{-1}b} \times \sqrt{b^{-1}c} \times \sqrt{c^{-1}a} \), we will simplify it step by step.

### Step 1: Rewrite the expression
We start by rewriting the expression using the property of square roots:
\[ \sqrt{a^{-1}b} = \frac{\sqrt{b}}{\sqrt{a}}, \quad \sqrt{b^{-1}c} = \frac{\sqrt{c}}{\sqrt{b}}, \quad \sqrt{c^{-1}a} = \frac{\sqrt{a}}{\sqrt{c}} \]
Thus, the expression becomes:
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