diff --git a/lib/unitsml/compose/builder.rb b/lib/unitsml/compose/builder.rb
index 335a03d..b600205 100644
--- a/lib/unitsml/compose/builder.rb
+++ b/lib/unitsml/compose/builder.rb
@@ -16,13 +16,10 @@ class << self
         # "/" and inverts b's power; `a * b` keeps "*"). An explicit trailing
         # extender on the left (from #extender) already is the join, so no glyph
         # is inserted after it — but `/` still inverts the right-hand side.
-        # An empty side inserts no glyph. invert_dimensions: false keeps
-        # Dimension leaves un-inverted on division (Quantity compatibility).
-        def build_product(left_terms, right_terms, operator,
-                          invert_dimensions: true)
+        # An empty side inserts no glyph.
+        def build_product(left_terms, right_terms, operator)
           left = build_terms(left_terms, invert: false)
-          right = build_terms(right_terms, invert: operator == "/",
-                                           invert_dimensions: invert_dimensions)
+          right = build_terms(right_terms, invert: operator == "/")
           joiner = join_glyph(left, right, operator)
           build_root_formula(left + joiner + right)
         end
@@ -33,7 +30,7 @@ def quantity_product(left, right, operator)
           return nil unless left || right
 
           build_product(left ? left.value : [], right ? right.value : [],
-                        operator, invert_dimensions: false)
+                        operator)
         end
 
         # Independent copy of a Formula (tree, powers, prefixes, text and
@@ -99,11 +96,8 @@ def build_root_formula(terms, metadata = nil)
         # Rebuild every operand: map_leaves reconstructs branch wrappers and
         # each Unit/Dimension leaf is copied with a freshly built final power
         # (and a duplicated prefix). Non-leaf terms (Extender/Number) plain-dup.
-        def build_terms(terms, invert:, invert_dimensions: true)
-          TermTree.map_leaves(terms) do |leaf|
-            rebuild_leaf(leaf, invert && (invert_dimensions ||
-                                          !leaf.is_a?(Dimension)))
-          end
+        def build_terms(terms, invert:)
+          TermTree.map_leaves(terms) { |leaf| rebuild_leaf(leaf, invert) }
         end
 
         def join_glyph(left, right, operator)
diff --git a/lib/unitsml/parser.rb b/lib/unitsml/parser.rb
index ca464fa..6b669d5 100644
--- a/lib/unitsml/parser.rb
+++ b/lib/unitsml/parser.rb
@@ -73,18 +73,28 @@ def update_units_exponents(array, inverse, sqrt = false)
           end
         end
 
-        case object
-        when Unit
-          next object.power_numerator = Number.new("0.5") if sqrt
-          next unless inverse
-
-          inverse ? object.inverse_power_numerator : object.power_numerator
-        when Dimension then object.power_numerator = Number.new("0.5") if sqrt
-        when Extender then inverse = !inverse if ["/", "//"].any?(object.symbol)
-        when Formula then update_units_exponents(object.value, inverse)
-        when Fenced then update_units_exponents([object.value], inverse, sqrt)
-        end
+        inverse = update_term_exponent(object, inverse, sqrt)
+      end
+    end
+
+    # Apply the sqrt/inverse state to one term; returns the inverse state for
+    # the next term (a "/" or "//" separator flips it).
+    def update_term_exponent(object, inverse, sqrt)
+      case object
+      when Unit, Dimension then update_leaf_exponent(object, inverse, sqrt)
+      when Extender then return !inverse if ["/", "//"].any?(object.symbol)
+      when Formula then update_units_exponents(object.value, inverse)
+      when Fenced then update_units_exponents([object.value], inverse, sqrt)
       end
+      inverse
+    end
+
+    # Units and dimensions follow the same rule: a sqrt sets the 0.5 exponent,
+    # otherwise a term after "/" has its exponent inverted.
+    def update_leaf_exponent(object, inverse, sqrt)
+      return object.power_numerator = Number.new("0.5") if sqrt
+
+      object.inverse_power_numerator if inverse
     end
 
     def post_extras
diff --git a/lib/unitsml/power_numerator.rb b/lib/unitsml/power_numerator.rb
index f75ee8b..be358df 100644
--- a/lib/unitsml/power_numerator.rb
+++ b/lib/unitsml/power_numerator.rb
@@ -17,6 +17,17 @@ def power_numerator=(power)
       @power_numerator = coerce_power_type(power)
     end
 
+    # Flip the exponent's sign in place for a term after "/" in a parsed
+    # string; no exponent becomes -1. Used by the parser for both units and
+    # dimensions.
+    def inverse_power_numerator
+      if power_numerator
+        power_numerator.update_negative_sign
+      else
+        @power_numerator = Number.new("-1")
+      end
+    end
+
     private
 
     # The exponent lexemes the library itself stores: an integer, an n/m or
diff --git a/lib/unitsml/unit.rb b/lib/unitsml/unit.rb
index 1289ee8..5cb4848 100644
--- a/lib/unitsml/unit.rb
+++ b/lib/unitsml/unit.rb
@@ -114,14 +114,6 @@ def downcase_system_type
       Lutaml::Model::Utils.snake_case(system_type)
     end
 
-    def inverse_power_numerator
-      if power_numerator
-        power_numerator.update_negative_sign
-      else
-        @power_numerator = Number.new("-1")
-      end
-    end
-
     private
 
     # Resolve a unit reference to a canonical symbol id, exactly like the parser
diff --git a/spec/unitsml/composite_spec.rb b/spec/unitsml/composite_spec.rb
index b1d8b95..f869f66 100644
--- a/spec/unitsml/composite_spec.rb
+++ b/spec/unitsml/composite_spec.rb
@@ -1,7 +1,6 @@
 # frozen_string_literal: true
 
 require "spec_helper"
-require "digest"
 
 # Composite-unit builder (issue #2): the operator DSL (Unit#* / Unit#/) and the
 # Unitsml.compose keyword form, both producing a root Formula whose output
@@ -678,8 +677,8 @@ def expect_parity(built, string)
       expect_parity(built, "W/m/s")
     end
 
-    it "keeps dimensions glyph-only, like the parser" do
-      built = Unitsml::Dimension.new("dim_M").ext("/").dimension("dim_L")
+    it "states dimension exponents explicitly after an extender, like units" do
+      built = Unitsml::Dimension.new("dim_M").ext("/").dimension("dim_L", -1)
       expect_parity(built, "dim_M/dim_L")
     end
 
@@ -1116,13 +1115,13 @@ def nil_side_results(formula)
       expect(copied.prefix).not_to be(leaf.prefix)
     end
 
-    it "keeps main's un-inverted dimension division" do
+    it "inverts dimension division like the parser" do
       result = builder.quantity_product(Unitsml.parse("dim_M"),
                                         Unitsml.parse("dim_L"), "/")
       xml = result.to_xml
       expect(xml).to eq(Unitsml.parse("dim_M/dim_L").to_xml)
-      expect(Digest::SHA256.hexdigest(xml)[0, 16]).to eq("fadb9a9811d67de4")
-      expect(result.value.last.power_numerator).to be_nil
+      expect(xml).to include('xml:id="D_L-1M"')
+      expect(result.value.last.power_numerator.raw_value).to eq("-1")
     end
 
     it "keeps the default DSL dimension inversion" do
@@ -1321,4 +1320,27 @@ def mutable_parts(formula)
       expect(formula.norm_text).to eq("s*m^(0)")
     end
   end
+
+  describe "parsed dimension division" do
+    {
+      "dim_L/dim_T" => "D_LT-1",
+      "dim_L/dim_T^2" => "D_LT-2",
+      "dim_M/dim_L^-3" => "D_L3M",
+    }.each do |text, id|
+      it "inverts the dimension after / in #{text.inspect}" do
+        expect(Unitsml.parse(text).to_xml).to include(%(xml:id="#{id}"))
+      end
+    end
+
+    it "matches the explicit negative exponent form" do
+      expect(Unitsml.parse("dim_L/dim_T").to_xml)
+        .to eq(Unitsml.parse("dim_L*dim_T^-1").to_xml)
+    end
+
+    it "gives dimension quantities the inverted text" do
+      length = Unitsml::Quantity.new(value: 2, unit: "dim_L")
+      time = Unitsml::Quantity.new(value: 1, unit: "dim_T")
+      expect((length / time).norm_text).to eq("dim_L*dim_T^(-1)")
+    end
+  end
 end