diff --git a/lib/ModelingToolkitTearing/src/tearingstate.jl b/lib/ModelingToolkitTearing/src/tearingstate.jl
index ac37575..31d5a1d 100644
--- a/lib/ModelingToolkitTearing/src/tearingstate.jl
+++ b/lib/ModelingToolkitTearing/src/tearingstate.jl
@@ -529,7 +529,7 @@ function __get_expression_sort_key!(
                     end
                     v = convert(Float64, v)
                     for t in arg_k
-                        push!(result, (t[1], t[2] ^ v * cf, t[3] + v))
+                        push!(result, (t[1], abs(t[2]) ^ v * cf, t[3] + v))
                     end
                     length(result) > 100 && break
                 end
@@ -546,7 +546,7 @@ function __get_expression_sort_key!(
                 @match args[2] begin
                     BSImpl.Const(; val) => if val isa Real
                         v = convert(Float64, val)
-                        return map(k -> (k[1], k[2] ^ v, k[3] + v), base_key)
+                        return map(k -> (k[1], abs(k[2]) ^ v, k[3] + v), base_key)
                     else
                         length(base_key) > 100 && return base_key
                         return vcat(base_key, get_expression_sort_key!(cache, args[2], var2idx, canonical_ranks))
diff --git a/lib/ModelingToolkitTearing/test/runtests.jl b/lib/ModelingToolkitTearing/test/runtests.jl
index 5ae2b00..b23214c 100644
--- a/lib/ModelingToolkitTearing/test/runtests.jl
+++ b/lib/ModelingToolkitTearing/test/runtests.jl
@@ -340,3 +340,11 @@ MTKTearing.is_timevarying_operator(::Op3) = true
     ci = MTKTearing.ClockInference(ts)
     @test_throws MTKTearing.ExpectedDiscreteClockPartitionError MTKTearing.infer_clocks!(ci)
 end
+
+@testset "Equation sorting does safe exponentiation" begin
+    # https://github.com/SciML/ModelingToolkit.jl/issues/4708
+    @variables x(t) y(t)
+    @named sys = System([D(x) ~ -x, y ~ (1 - 2x)^0.5], t)
+    # This used to run `(-2) ^ 0.5` which hit a `DomainError`
+    @test_nowarn mtkcompile(sys)
+end