Avoid convert in ^

src/intervals/arithmetic/power.jl

@@ -60,10 +60,12 @@ function Base.:^(x::Interval, y::Interval)
     return _unsafe_interval(bareinterval(r), d, t)
 end
 
-Base.:^(n::Integer, y::Interval) = ^(n//one(n), y)
-Base.:^(x::Interval, n::Integer) = ^(x, n//one(n))
-Base.:^(x::Rational, y::Interval) = ^(convert(Interval{typeof(x)}, x), y)
-Base.:^(x::Interval, y::Rational) = ^(x, convert(Interval{typeof(y)}, y))
+Base.:^(n::Integer, y::Interval) = _select_pow(power_mode(), n, y)
+Base.:^(x::Interval, n::Integer) = _select_pow(power_mode(), x, n)
+Base.:^(x::Rational, y::Interval) = _select_pow(power_mode(), x, y)
+Base.:^(x::Interval, y::Rational) = _select_pow(power_mode(), x, y)
+Base.:^(x::AbstractFloat, y::Interval) = _select_pow(power_mode(), x, y)
+Base.:^(x::Interval, y::AbstractFloat) = _select_pow(power_mode(), x, y)
 
 # overwrite behaviour for small integer powers from https://github.com/JuliaLang/julia/pull/24240
 Base.literal_pow(::typeof(^), x::Interval, ::Val{n}) where {n} = x^n
@@ -130,8 +132,6 @@ function pow(x::BareInterval{T}, y::BareInterval{S}) where {T<:NumTypes,S<:Ratio
     return BareInterval{R}(hull(_pow(x, inf(y)), _pow(x, sup(y))))
 end
 
-pow(n::Integer, y::BareInterval) = pow(n//one(n), y)
-pow(x::BareInterval, n::Integer) = pow(x, n//one(n))
 pow(x::Real, y::BareInterval) = pow(bareinterval(x), y)
 pow(x::BareInterval, y::Real) = pow(x, bareinterval(y))
 
@@ -145,8 +145,6 @@ function pow(x::Interval, y::Interval)
     return _unsafe_interval(r, d, t)
 end
 
-pow(n::Integer, y::Interval) = pow(n//one(n), y)
-pow(x::Interval, n::Integer) = pow(x, n//one(n))
 pow(x::Real, y::Interval) = pow(interval(x), y)
 pow(x::Interval, y::Real) = pow(x, interval(y))