In this paper, we study symmetry properties of positive solutions to the fractional Laplace equation with negative powers on the whole space. We can use the direct method of moving planes introduced by Jarohs-Weth-Chen-Li-Li to prove one particular result below. If
$(-Δ)^{α/2}u(x)+u^{-β}(x) = 0, \ \ \ x∈ \mathbb{R}^n, $
with the growth/decay property
$u(x) = a|x|^{m}+o(1), \ \ as \ \ |x| \to ∞, $
where
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