diff --git a/src/Infinities.jl b/src/Infinities.jl
index fa5bf55..2af22a9 100644
--- a/src/Infinities.jl
+++ b/src/Infinities.jl
@@ -1,11 +1,11 @@
 module Infinities
 
 import Base: angle, isone, iszero, isinf, isfinite, abs, one, oneunit, zero, isless, inv,
-                +, -, *, ==, <, ≤, >, ≥, fld, cld, div, mod, min, max, sign, signbit,
+                +, -, *, ^, ==, <, ≤, >, ≥, fld, cld, div, mod, min, max, sign, signbit,
                 string, show, promote_rule, convert, getindex,
                 Bool, Integer
 
-export ∞,  ℵ₀,  ℵ₁, RealInfinity, ComplexInfinity, InfiniteCardinal, NotANumber
+export ∞,  ℵ₀,  ℵ₁, RealInfinity, ComplexInfinity, InfiniteCardinal, NotANumber, PositiveInfinity, NegativeInfinity
 # The following is commented out for now to avoid conflicts with Infinity.jl
 # export Infinity
 
@@ -45,13 +45,18 @@ oneunit(::Infinity) = 1
 zero(::Infinity) = 0
 zero(::Type{Infinity}) = 0
 
-struct RealInfinity <: Real
-    signbit::Bool
-end
+abstract type RealInfinity <: Real end
+struct PositiveInfinity <: RealInfinity end
+struct NegativeInfinity <: RealInfinity end
+
+signbit(::PositiveInfinity) = false
+signbit(::NegativeInfinity) = true
+one(::RealInfinity) = 1.0
 
-RealInfinity() = RealInfinity(false)
-RealInfinity(::Infinity) = RealInfinity()
+RealInfinity() = PositiveInfinity()
+RealInfinity(::Infinity) = PositiveInfinity()
 RealInfinity(x::RealInfinity) = x
+RealInfinity(x::Bool) = ifelse(x, NegativeInfinity(), PositiveInfinity())
 
 _convert(::Type{Float16}, x::RealInfinity) = sign(x)*Inf16
 _convert(::Type{Float32}, x::RealInfinity) = sign(x)*Inf32
@@ -63,7 +68,6 @@ for Typ in (RealInfinity, Infinity)
     @eval Bool(x::$Typ) = throw(InexactError(:Bool, Bool, x)) # ambiguity fix
 end
 
-signbit(y::RealInfinity) = y.signbit
 sign(y::RealInfinity) = 1-2signbit(y)
 angle(x::RealInfinity) = π*signbit(x)
 
diff --git a/src/algebra.jl b/src/algebra.jl
index 7311748..669cc4a 100644
--- a/src/algebra.jl
+++ b/src/algebra.jl
@@ -1,14 +1,17 @@
 @inline infpromote(x, y) = Base._promote(x, y)
 @inline infpromote(x::ExtendedComplex, y::AllInfinities) = (x, ComplexInfinity(y))
 @inline infpromote(x::ExtendedComplex, y::ComplexInfinity) = Base._promote(x, y)
-@inline infpromote(x::Real, y::InfiniteCardinal) = (x, ∞)
+@inline infpromote(x::Real, ::InfiniteCardinal) = (x, ∞)
 @inline infpromote(x::Integer, y::InfiniteCardinal) = (x, y)
+@inline infpromote(x::RealInfinity, y::Union{Integer, Rational}) = (x, float(y))
+@inline infpromote(x::Union{Integer, Rational}, y::RealInfinity) = (float(x), y)
+@inline infpromote(x::RealInfinity, ::InfiniteCardinal) = (x, ∞)
 
 
 # sign
 +(::Infinity) = RealInfinity()
 -(::Infinity) = RealInfinity(true)
--(y::RealInfinity) = RealInfinity(!y.signbit)
+-(y::RealInfinity) = RealInfinity(!signbit(y))
 -(y::ComplexInfinity{B}) where B<:Integer = sign(y) == 1 ? ComplexInfinity(one(B)) : ComplexInfinity(zero(B))
 +(x::InfiniteCardinal) = x
 -(::InfiniteCardinal) = -∞
@@ -88,7 +91,18 @@ for OP in (:fld,:cld,:div)
     end
 end
 
-# Base.literal_pow
+# power
+# Although the base implementation can cover these cases, it can change overtime and yield inconsistent results.
+# ref: https://github.com/JuliaMath/Infinities.jl/actions/runs/19993302836/
+_infpow(::PositiveInfinity, p) = ifelse(iszero(p), one(p), ifelse(p > 0, +∞, +zero(p)))
+function _infpow(x::NegativeInfinity, p)
+    !isinteger(p) && throw(Base.Math.throw_exp_domainerror(x))
+    iszero(p) && return one(p)
+    isodd(p) && return ifelse(p > 0, -∞, -zero(p))
+    return ifelse(p > 0, +∞, +zero(p))
+end
+^(x::RealInfinity, p::Real) = _infpow(infpromote(x, p)...)
+^(x::RealInfinity, p::Integer) = _infpow(infpromote(x, p)...)
 
 # inv
 inv(::Union{Infinity,InfiniteCardinal}) = 0
diff --git a/src/ambiguities.jl b/src/ambiguities.jl
index 2ca1ead..719df67 100644
--- a/src/ambiguities.jl
+++ b/src/ambiguities.jl
@@ -27,6 +27,8 @@ for Typ in (Complex, Rational, Complex{Bool}, Integer)
     @eval *(x::$Typ, y::AllInfinities) = _mul(x, y)
 end
 
+^(x::RealInfinity, y::Rational) = _infpow(infpromote(x, y)...)
+
 for Typ in (Rational, )
     @eval mod(::IntegerInfinities, ::$Typ) = NotANumber()
     @eval mod(x::$Typ, y::IntegerInfinities) = _mod(x, y)
diff --git a/src/interface.jl b/src/interface.jl
index b9ebc60..9d4168c 100644
--- a/src/interface.jl
+++ b/src/interface.jl
@@ -7,8 +7,8 @@ iszero(::AllInfinities) = false
 isinf(::AllInfinities) = true
 isfinite(::AllInfinities) = false
 
-promote_rule(::Type{Infinity}, ::Type{RealInfinity}) = RealInfinity # not detected by CodeCov. Removing this results in failed tests.
+promote_rule(::Type{Infinity}, ::Type{<:RealInfinity}) = RealInfinity # not detected by CodeCov. Removing this results in failed tests.
 promote_rule(::Type{Infinity}, ::Type{ComplexInfinity{T}}) where T = ComplexInfinity{T}
-promote_rule(::Type{RealInfinity}, ::Type{ComplexInfinity{T}}) where T = ComplexInfinity{T}
-promote_rule(::Type{ComplexInfinity{T}}, ::Type{RealInfinity}) where T<:Integer = ComplexInfinity{T}
+promote_rule(::Type{<:RealInfinity}, ::Type{ComplexInfinity{T}}) where T = ComplexInfinity{T}
+promote_rule(::Type{ComplexInfinity{T}}, ::Type{<:RealInfinity}) where T<:Integer = ComplexInfinity{T}
 promote_rule(::Type{ComplexInfinity{T}}, ::Type{ComplexInfinity{S}}) where {T, S} = ComplexInfinity{promote_type(T, S)}
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 29344e4..610b384 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -177,6 +177,29 @@ using Aqua
         @test (-∞)*2 ≡ 2*(-∞) ≡ -2 * ∞ ≡ ∞ * (-2) ≡ (-2) * RealInfinity() ≡ -∞
         @test (-∞)*2.3 ≡ 2.3*(-∞) ≡ -2.3 * ∞ ≡ ∞ * (-2.3) ≡ (-2.3) * RealInfinity() ≡ -∞
 
+        @testset "power" begin
+            # zero
+            @test (+∞)^0.0 ≡ (-∞)^0.0 ≡ 1.0
+
+            # positive even/odd/fraction
+            @test (+∞)^2.0 ≡ (-∞)^2.0 ≡ +∞
+            @test (+∞)^1.0 ≡ +∞
+            @test (-∞)^1.0 ≡ -∞
+            @test (+∞)^0.5 ≡ +∞
+            @test_throws DomainError (-∞)^0.5
+
+            # negative even/odd/fraction
+            @test (+∞)^(-2.0) ≡ (-∞)^(-2.0) ≡ 0.0
+            @test (+∞)^(-1.0) ≡ 0.0
+            @test (-∞)^(-1.0) ≡ -0.0
+            @test (+∞)^(-0.5) ≡ 0.0
+            @test_throws DomainError (-∞)^(-0.5)
+
+            # irrational
+            @test (+∞)^π ≡ +∞
+            @test_throws DomainError (-∞)^π
+        end
+
         @test isinf(-∞)
         @test !isfinite(-∞)
 
@@ -301,14 +324,26 @@ using Aqua
         @test Base.literal_pow(^, ℵ₀, Val(0)) ≡ ℵ₀^0 ≡ 1
         @test Base.literal_pow(^, ℵ₀, Val(1)) ≡ ℵ₀^1 ≡ ℵ₀
         @test Base.literal_pow(^, ℵ₀, Val(-1)) ≡ ℵ₀^(-1) ≡ 0
+        @test Base.literal_pow(^, ℵ₀, Val(2)) ≡ ℵ₀^2 ≡ ℵ₀
+        @test Base.literal_pow(^, ℵ₀, Val(-2)) ≡ ℵ₀^(-2) ≡ 0
 
         @test Base.literal_pow(^, ∞, Val(0)) ≡ ∞^0 ≡ 1
         @test Base.literal_pow(^, ∞, Val(1)) ≡ ∞^1 ≡ ∞
         @test Base.literal_pow(^, ∞, Val(-1)) ≡ ∞^(-1) ≡ 0
+        @test Base.literal_pow(^, ∞, Val(2)) ≡ ∞^2 ≡ ∞
+        @test Base.literal_pow(^, ∞, Val(-2)) ≡ ∞^(-2) ≡ 0
+
+        @test Base.literal_pow(^, +∞, Val(0)) ≡ (+∞)^0 ≡ 1.0
+        @test Base.literal_pow(^, +∞, Val(1)) ≡ (+∞)^1 ≡ +∞
+        @test Base.literal_pow(^, +∞, Val(-1)) ≡ (+∞)^(-1) ≡ 0.0
+        @test Base.literal_pow(^, +∞, Val(2)) ≡ (+∞)^2 ≡ +∞
+        @test Base.literal_pow(^, +∞, Val(-2)) ≡ (+∞)^(-2) ≡ 0.0
 
         @test Base.literal_pow(^, -∞, Val(0)) ≡ (-∞)^0 ≡ 1.0
         @test Base.literal_pow(^, -∞, Val(1)) ≡ (-∞)^1 ≡ -∞
         @test Base.literal_pow(^, -∞, Val(-1)) ≡ (-∞)^(-1) ≡ (VERSION < v"1.12-" ?  0.0 : -0.0)
+        @test Base.literal_pow(^, -∞, Val(2)) ≡ (-∞)^2 ≡ +∞
+        @test Base.literal_pow(^, -∞, Val(-2)) ≡ (-∞)^(-2) ≡ 0.0
 
         @test Base.literal_pow(^, ComplexInfinity(0.1), Val(0)) ≡ ComplexInfinity(0.1)^0 ≡ 1.0+0.0im
         @test Base.literal_pow(^, ComplexInfinity(0.1), Val(1)) ≡ (ComplexInfinity(0.1))^1 ≡ ComplexInfinity(0.1)
diff --git a/test/test_ambiguity.jl b/test/test_ambiguity.jl
index c2ebeb5..03e2119 100644
--- a/test/test_ambiguity.jl
+++ b/test/test_ambiguity.jl
@@ -17,4 +17,27 @@
         @test fld(inf, 1//2) ≡ cld(inf, 1//2) ≡ div(inf, 1//2) ≡ inf
         @test fld(inf, ∞) ≡ fld(inf, +∞) ≡ fld(inf, ℵ₀) ≡ fld(inf, ComplexInfinity()) ≡ NotANumber()
     end
+
+    @testset "rational power" begin
+        # zero
+        @test (+∞)^(0//1) ≡ (-∞)^(0//1) ≡ 1.0
+
+        # positive even/odd/fraction
+        @test (+∞)^(2//1) ≡ (-∞)^(2//1) ≡ +∞
+        @test (+∞)^(1//1) ≡ +∞
+        @test (-∞)^(1//1) ≡ -∞
+        @test (+∞)^(1//2) ≡ +∞
+        @test_throws DomainError (-∞)^(1//2)
+
+        # negative even/odd/fraction
+        @test (+∞)^(-2.0) ≡ (-∞)^(-2.0) ≡ 0.0
+        @test (+∞)^(-1//1) ≡ 0.0
+        @test (-∞)^(-1//1) ≡ -0.0
+        @test (+∞)^(-1//2) ≡ 0.0
+        @test_throws DomainError (-∞)^(-1//2)
+
+        # irrational
+        @test (+∞)^π ≡ +∞
+        @test_throws DomainError (-∞)^π
+    end
 end
\ No newline at end of file