Let $f(x,y)=x^n y^m=P$. If $x$ is doubled and $y$ is halved, the new value of $f$ is

$2^{n-m}P$
$2^{m-n}P$
$2(n-m)P$
$2(m-n)P$

Correct answer: $2^{n-m}P$

Solution

If $x$ becomes $2x$ and $y$ becomes $y/2$, then the new value is $(2x)^n(y/2)^m=2^n x^n\cdot 2^{-m}y^m=2^{n-m}x^ny^m=2^{n-m}P$. So the correct option is $2^{n-m}P$.

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