diff --git a/arith.modal b/arith.modal
index 96d91e5..def6e92 100644
--- a/arith.modal
+++ b/arith.modal
@@ -331,7 +331,7 @@
 <> ((pow (Z (- ?x)) (N (0 ?k)))) ((nat>pos (pow (N ?x) (N (0 ?k)))))
 <> ((pow (Z (- ?x)) (N (1 ?k)))) ((nat>neg (pow (N ?x) (N (1 ?k)))))
 
--- ( to natural number )
+-- ( to integer )
 <> ((int ?*)) ((int1 (?*)))
 <> ((int1 (- ?t))) ((int2 - (nat1 ?t)))
 <> ((int1 (?h ?t))) ((int2 + (nat1 (?h ?t))))
@@ -375,4 +375,15 @@
 
 <> ((div (Q (?s ?x ?d)) (Q (?t ?y ?e)))) ((mul (Q (?s ?x ?d)) (Q (?t ?e ?y))))
 
-(str (mul (Q (+ sixteen ten)) (Q (- sixteen ten))))
+<> ((pow (Q (?s ?x ?d)) (N ?k))) ((qpow (pow (Z (?s ?x)) (N ?k)) (pow (N ?d) (N ?k))))
+<> ((qpow (Z (?s ?n)) (N ?d))) ((ratify ?s (N ?n) (N ?d)))
+
+-- ( to rational number )
+<> ((rat ?*)) ((rat1 (?*)))
+<> ((rat1 (- ?t))) ((rat2 - ?t ()))
+<> ((rat1 (?h ?t))) ((rat2 + (?h ?t) ()))
+<> ((rat2 ?s (/ ?t) ?a)) ((rat3 ?s (nat1 reverse ?a) (nat1 ?t)))
+<> ((rat2 ?s (?h ?t) ?a)) ((rat2 ?s ?t (?h ?a)))
+<> ((rat3 ?s (N ?n) (N ?d))) ((Q (?s ?n ?d)))
+
+(str (pow (rat -2/7) (nat 3)))