diff --git a/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/optimizer/float.rkt b/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/optimizer/float.rkt
index b39b475022..2a6400842c 100644
--- a/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/optimizer/float.rkt
+++ b/pkgs/typed-racket-pkgs/typed-racket-lib/typed-racket/optimizer/float.rkt
@@ -15,7 +15,7 @@
   (mk-unsafe-tbl generic "fl~a" "unsafe-fl~a"))
 
 (define binary-float-ops
-  (mk-float-tbl (list #'+ #'- #'* #'/ #'min #'max)))
+  (mk-float-tbl (list #'+ #'- #'* #'/ #'min #'max #'expt)))
 (define binary-float-comps
   (dict-set*
     (mk-float-tbl (list #'= #'<= #'< #'> #'>=))
diff --git a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/missed-optimizations/fixnum.rkt b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/missed-optimizations/fixnum.rkt
index 82a5a0a45a..1ca6c29dd7 100644
--- a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/missed-optimizations/fixnum.rkt
+++ b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/missed-optimizations/fixnum.rkt
@@ -4,6 +4,8 @@ TR info: fixnum.rkt 12:0 (fx* (values (ann x Index)) (values (ann y Index))) --
 TR info: fixnum.rkt 15:0 (fx+ (+ 300 301) (+ 301 302)) -- non-optimized fixnum op
 TR info: fixnum.rkt 16:0 (fxquotient -4 -5) -- non-optimized fixnum op
 TR info: fixnum.rkt 44:28 (- 1 (expt 2 (- (system-type (quote word)) 2))) -- possible exact real arith
+TR info: fixnum.rkt 44:33 (expt 2 (- (system-type (quote word)) 2)) -- possible exact real arith
+TR info: fixnum.rkt 45:28 (expt 2 (- (system-type (quote word)) 2)) -- possible exact real arith
 TR missed opt: fixnum.rkt 10:0 (+ (ann z Fixnum) 234) -- out of fixnum range
 TR missed opt: fixnum.rkt 11:0 (* (ann x Index) (ann y Index)) -- out of fixnum range
 TR missed opt: fixnum.rkt 14:0 (+ (+ 300 301) (+ 301 302)) -- out of fixnum range
diff --git a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/exact-inexact.rkt b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/exact-inexact.rkt
index 997f1a4cf3..904cbaa226 100644
--- a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/exact-inexact.rkt
+++ b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/exact-inexact.rkt
@@ -1,10 +1,14 @@
 #;#;
 #<<END
+TR missed opt: exact-inexact.rkt 8:16 (expt 1.0f0 2.0f0) -- all args float-arg-expr, result not Float -- caused by: 8:22 1.0f0, 8:28 2.0f0
+TR missed opt: exact-inexact.rkt 9:21 (expt 1.0f0 2.0f0) -- all args float-arg-expr, result not Float -- caused by: 9:27 1.0f0, 9:33 2.0f0
 TR opt: exact-inexact.rkt 2:0 (exact->inexact (expt 10 100)) -- int to float
 TR opt: exact-inexact.rkt 3:0 (round (exact->inexact (expt 2.3 3.2))) -- unary float
+TR opt: exact-inexact.rkt 3:23 (expt 2.3 3.2) -- binary float
 TR opt: exact-inexact.rkt 3:7 (exact->inexact (expt 2.3 3.2)) -- float to float
 TR opt: exact-inexact.rkt 4:0 (real->double-flonum (expt 10 100)) -- int to float
 TR opt: exact-inexact.rkt 5:0 (round (real->double-flonum (expt 2.3 3.2))) -- unary float
+TR opt: exact-inexact.rkt 5:28 (expt 2.3 3.2) -- binary float
 TR opt: exact-inexact.rkt 5:7 (real->double-flonum (expt 2.3 3.2)) -- float to float
 TR opt: exact-inexact.rkt 8:0 (exact->inexact (expt 1.0f0 2.0f0)) -- single-float to single-float
 TR opt: exact-inexact.rkt 9:0 (real->single-flonum (expt 1.0f0 2.0f0)) -- single-float to single-float
diff --git a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/expt.rkt b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/expt.rkt
index 1f16401e6a..5f9942fd43 100644
--- a/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/expt.rkt
+++ b/pkgs/typed-racket-pkgs/typed-racket-test/tests/typed-racket/optimizer/tests/expt.rkt
@@ -1,9 +1,15 @@
 #;#;
 #<<END
 TR missed opt: expt.rkt 6:13 (expt (sin 0.25) 1.0) -- unexpected complex type
+TR missed opt: expt.rkt 9:0 (expt -2.0 0.5) -- unexpected complex type
 TR opt: expt.rkt 6:19 (sin 0.25) -- unary float
+TR opt: expt.rkt 8:0 (expt 2.0 3.0) -- binary float
+END
+#<<END
+8.0
+8.659560562354934e-17+1.4142135623730951i
+
 END
-""
 #lang typed/racket
 #reader tests/typed-racket/optimizer/reset-port
 
@@ -12,3 +18,6 @@ END
 ;; this let to incorrect optimization
 (define (crash)
   (real-part (expt (sin 0.25) 1.0)))
+
+(expt 2.0 3.0)
+(expt -2.0 0.5) ; not a valid optimization, returns a complex