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LCM of Polynomials

If ap=x, aq...

Question

If $a^{p} = x, a^{q} = y, x^{q} y^{p} = a^{2 / r}$ then pqr = ___

A

1

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B

-1

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C

x^{- 1 / p}

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D

x^{p}

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Solution

The correct option is A 1
$a^{p} = x, a^{q} = y$
$x^{q} y^{p} = a^{2 / r}$
$\Rightarrow (a^{p q}) (a^{q p}) = a^{2 / r}$
$\Rightarrow a^{2 p q} = a^{2 / r}$
$\Rightarrow 2 p q = 2 / r$
$\Rightarrow p q r = 1$

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