diff --git a/src/Symbolics/drop_powers.jl b/src/Symbolics/drop_powers.jl
index 6919cc5..55def58 100644
--- a/src/Symbolics/drop_powers.jl
+++ b/src/Symbolics/drop_powers.jl
@@ -13,6 +13,11 @@ julia>drop_powers((x+y)^2 + (x+y)^3, [x,y], 3)
 x^2 + y^2 + 2*x*y
 ```
 """
+function drop_powers(expr::BasicSymbolic, vars::Vector{<:BasicSymbolic}, deg::Int)
+    return unwrap(drop_powers(Num(expr), Num.(vars), deg))
+end
+
+# Num fallback: the actual implementation
 function drop_powers(expr::Num, vars::Vector{Num}, deg::Int)
     Symbolics.@variables ϵ
     subs_expr = deepcopy(expr)
@@ -43,19 +48,25 @@ function drop_powers(eqs::Vector{Equation}, var::Vector{Num}, deg::Int)
         Equation(drop_powers(eq.lhs, var, deg), drop_powers(eq.rhs, var, deg)) for eq in eqs
     ]
 end
+function drop_powers(expr::BasicSymbolic, var::BasicSymbolic, deg::Int)
+    drop_powers(expr, [var], deg)
+end
 drop_powers(expr, var::Num, deg::Int) = drop_powers(expr, [var], deg)
-drop_powers(x, vars, deg::Int) = drop_powers(wrap(x), vars, deg)
-# ^ TODO: in principle `drop_powers` should get in BasicSymbolic and have a fallback for Num
+drop_powers(x, vars, deg::Int) = drop_powers(Num(x), Num.(vars), deg)
 
 "Return the highest power of `y` occurring in the term `x`."
-function max_power(x::Num, y::Num)
+function max_power(x::BasicSymbolic, y::BasicSymbolic)
     terms = get_all_terms(x)
     powers = power_of.(terms, y)
     return maximum(powers)
 end
 
+# Num fallback: unwrap to BasicSymbolic
+max_power(x::Num, y::Num) = max_power(unwrap(x), unwrap(y))
+max_power(x::BasicSymbolic, y::Num) = max_power(x, unwrap(y))
 max_power(x::Vector{Num}, y::Num) = maximum(max_power.(x, y))
 max_power(x::Complex, y::Num) = maximum(max_power.([x.re, x.im], y))
+max_power(x::Num, y::BasicSymbolic) = max_power(unwrap(x), y)
 max_power(x, t) = max_power(wrap(x), wrap(t))
 
 "Return the power of `y` in the term `x`"
diff --git a/test/symbolics.jl b/test/symbolics.jl
index 3044f5d..5ffbf0c 100644
--- a/test/symbolics.jl
+++ b/test/symbolics.jl
@@ -1,6 +1,6 @@
 using Test
 using Symbolics
-using SymbolicUtils: Fixpoint, Prewalk, PassThrough, BasicSymbolic
+using SymbolicUtils: Fixpoint, Prewalk, PassThrough, BasicSymbolic, unwrap
 
 using QuestBase: @eqtest
 
@@ -59,6 +59,20 @@ end
 
     @eqtest drop_powers([a^2 + a + b, b], a, 2) == [a + b, b]
     @eqtest drop_powers([a^2 + a + b, b], [a, b], 2) == [a + b, b]
+
+    @testset "BasicSymbolic" begin
+        using SymbolicUtils: @syms
+
+        @syms a_bs b_bs
+
+        @test max_power(a_bs^2 + b_bs, a_bs) == 2
+        @test max_power(a_bs * ((a_bs + b_bs)^4)^2 + a_bs, a_bs) == 9
+
+        @test isequal(drop_powers(a_bs^2 + b_bs, a_bs, 2), b_bs)
+        @test isequal(drop_powers((a_bs + b_bs)^2, a_bs, 1), b_bs^2)
+        @test isequal(drop_powers((a_bs + b_bs)^2, [a_bs, b_bs], 2), unwrap(Num(0)))
+        @test drop_powers(a_bs^2 + b_bs, a_bs, 2) isa BasicSymbolic
+    end
 end
 
 @testset "trig_to_exp and exp_to_trig" begin