If $a^{x} = b^{y} = (a b)^{x y},$ then $x + y =$ ..............

1

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x y

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(a b)^{x + y}

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a b

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Solution

The correct option is D $1$
Given that , $a^{x} = b^{y} . . . . . (1)$

Hence, $(a b)^{x y}$

$= a^{x y} . b^{x y}$

$= (a^{x})^{y} . (b^{y})^{x} . . . . . (2)$

Substitute (1) in (2),

$(a^{x})^{y} . (a^{x})^{x}$

= $(a^{x})^{x + y} . . . . . (3)$

From equation (1) $x + y = 1$

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