diff --git a/g16ckt/src/gadgets/bn254/fp254impl.rs b/g16ckt/src/gadgets/bn254/fp254impl.rs
index 39b2aa2..84a16f4 100644
--- a/g16ckt/src/gadgets/bn254/fp254impl.rs
+++ b/g16ckt/src/gadgets/bn254/fp254impl.rs
@@ -696,7 +696,11 @@ pub trait Fp254Impl {
         exp: &BigUint,
     ) -> BigIntWires {
         if exp.is_zero() {
-            return BigIntWires::new_constant(a.len(), &BigUint::one()).unwrap();
+            // a^0 => 1 and Mont(1) => ark::Fq(R)
+            let r = ark_bn254::Fq::from(Self::montgomery_r_as_biguint())
+                .into_bigint()
+                .into();
+            return BigIntWires::new_constant(Self::N_BITS, &r).unwrap();
         }
 
         if exp.is_one() {
diff --git a/g16ckt/src/gadgets/bn254/fq.rs b/g16ckt/src/gadgets/bn254/fq.rs
index 8f1cb04..d759ed1 100644
--- a/g16ckt/src/gadgets/bn254/fq.rs
+++ b/g16ckt/src/gadgets/bn254/fq.rs
@@ -680,6 +680,33 @@ pub(super) mod tests {
         assert_eq!(result.output_value.value, expected_c);
     }
 
+    #[test]
+    fn test_exp_by_constant_montgomery() {
+        let a_v = rnd();
+
+        // test for random input
+        let k = rnd().into_bigint();
+        let expected_c = a_v.pow(k);
+        let input = FqInput::new([Fq::as_montgomery(a_v)]);
+        let result =
+            CircuitBuilder::streaming_execute::<_, _, FqOutput>(input, 10_000, |ctx, input| {
+                let [aa_wire] = input;
+                Fq::exp_by_constant_montgomery(ctx, aa_wire, &k.into())
+            });
+        assert_eq!(result.output_value.value, Fq::as_montgomery(expected_c));
+
+        // test for zero exponent
+        let k: ark_ff::BigInt<4> = ark_ff::BigInt::zero();
+        let expected_c = a_v.pow(k);
+        let input = FqInput::new([Fq::as_montgomery(a_v)]);
+        let result =
+            CircuitBuilder::streaming_execute::<_, _, FqOutput>(input, 10_000, |ctx, input| {
+                let [aa_wire] = input;
+                Fq::exp_by_constant_montgomery(ctx, aa_wire, &k.into())
+            });
+        assert_eq!(result.output_value.value, Fq::as_montgomery(expected_c));
+    }
+
     #[test]
     fn test_fq_multiplexer() {
         let w = 1;