Question

$\sqrt{x {}^{p - q } } \times \sqrt{x} {}^{q - a} \times \sqrt{x {}^{a - p} } =$
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Answer 1

$\sqrt{ {x}^{p - q} } \times \sqrt{ {x}^{q - a} } \times \sqrt{ {x}^{a - p} }$

According to Law of Exponent.

If

${x}^{a} \times {x}^{b }= {x}^{a + b}$

Using This.

$\sqrt{ {x}^{p - q} } \times \sqrt{ {x}^{q - a} } \times \sqrt{ {x}^{a - p} } \\ \\ = \sqrt{ {x}^{(p - q) + (q - a) + (a - p)} } \\ \\ = \sqrt{ {x}^{ \cancel{p} - q + q - a + a \cancel{ - p}} } \\ \\ = \sqrt{ {x}^{ \cancel{- q} + \cancel{q} - a + a} } \\ \\ = \sqrt{ {x}^{ \cancel{- a }+ \cancel{a}} } \\ \\ = \sqrt{ {x}^{0} }$

As we

${x}^{0} = 1$

So,

$\sqrt{ {x}^{0} } \\ \\ \sqrt{1} \\ \\ = 1$

$\underline{ \mathbf{Answer = 1}}$