diff --git a/src/gadgets/arithmetic.rs b/src/gadgets/arithmetic.rs
index 4d9ece34..124bcccb 100644
--- a/src/gadgets/arithmetic.rs
+++ b/src/gadgets/arithmetic.rs
@@ -112,11 +112,12 @@ impl<F: Extendable<D>, const D: usize> CircuitBuilder<F, D> {
         base: Target,
         exponent_bits: impl Iterator<Item = impl Borrow<Target>>,
     ) -> Target {
+        let zero = self.zero();
         let gate = ExponentiationGate::new(self.config.clone());
         let num_power_bits = gate.num_power_bits;
         let mut exp_bits_vec: Vec<Target> = exponent_bits.map(|b| *b.borrow()).collect();
         while exp_bits_vec.len() < num_power_bits {
-            exp_bits_vec.push(self.constant(F::ZERO));
+            exp_bits_vec.push(zero);
         }
         let gate_index = self.add_gate(gate.clone(), vec![]);
 
diff --git a/src/gates/exponentiation.rs b/src/gates/exponentiation.rs
index a1a7d5cd..697803c2 100644
--- a/src/gates/exponentiation.rs
+++ b/src/gates/exponentiation.rs
@@ -29,8 +29,9 @@ impl<F: Extendable<D>, const D: usize> ExponentiationGate<F, D> {
     }
 
     fn max_power_bits(num_wires: usize, num_routed_wires: usize) -> usize {
-        let max_for_routed_wires = num_routed_wires - 3;
-        let max_for_wires = (num_wires - 3) / 2;
+        // 2 wires are reserved for the base and output.
+        let max_for_routed_wires = num_routed_wires - 2;
+        let max_for_wires = (num_wires - 2) / 2;
         max_for_routed_wires.min(max_for_wires)
     }
 
@@ -147,7 +148,7 @@ impl<F: Extendable<D>, const D: usize> Gate<F, D> for ExponentiationGate<F, D> {
 
         let mut constraints = Vec::new();
 
-        let one = builder.constant_extension(F::Extension::ONE);
+        let one = builder.one_extension();
         for i in 0..self.num_power_bits {
             let prev_intermediate_value = if i == 0 {
                 one