diff --git a/benches/bigint.rs b/benches/bigint.rs
index f2d0fc5d..4e168602 100644
--- a/benches/bigint.rs
+++ b/benches/bigint.rs
@@ -4,7 +4,7 @@
 extern crate test;
 
 use num_bigint::{BigInt, BigUint, RandBigInt};
-use num_traits::{FromPrimitive, Num, One, Pow, Zero};
+use num_traits::{FromPrimitive, Num, One, Zero};
 use rand::rngs::StdRng;
 use rand::SeedableRng;
 use std::mem::replace;
@@ -327,16 +327,35 @@ fn hash(b: &mut Bencher) {
 #[bench]
 fn pow_bench(b: &mut Bencher) {
     b.iter(|| {
-        let upper = 100_usize;
-        for i in 2..=upper {
+        let upper = 100_u32;
+        let mut i_big = BigUint::from(1u32);
+        for _i in 2..=upper {
+            i_big += 1u32;
             for j in 2..=upper {
-                let i_big = BigUint::from_usize(i).unwrap();
                 i_big.pow(j);
             }
         }
     });
 }
 
+#[bench]
+fn pow_bench_bigexp(b: &mut Bencher) {
+    use num_traits::Pow;
+
+    b.iter(|| {
+        let upper = 100_u32;
+        let mut i_big = BigUint::from(1u32);
+        for _i in 2..=upper {
+            i_big += 1u32;
+            let mut j_big = BigUint::from(1u32);
+            for _j in 2..=upper {
+                j_big += 1u32;
+                Pow::pow(&i_big, &j_big);
+            }
+        }
+    });
+}
+
 /// This modulus is the prime from the 2048-bit MODP DH group:
 /// https://tools.ietf.org/html/rfc3526#section-3
 const RFC3526_2048BIT_MODP_GROUP: &str = "\
diff --git a/benches/roots.rs b/benches/roots.rs
index 62c32f2d..e6113136 100644
--- a/benches/roots.rs
+++ b/benches/roots.rs
@@ -4,7 +4,6 @@
 extern crate test;
 
 use num_bigint::{BigUint, RandBigInt};
-use num_traits::Pow;
 use rand::rngs::StdRng;
 use rand::SeedableRng;
 use test::Bencher;
diff --git a/ci/big_quickcheck/src/lib.rs b/ci/big_quickcheck/src/lib.rs
index 57451478..e5768ed1 100644
--- a/ci/big_quickcheck/src/lib.rs
+++ b/ci/big_quickcheck/src/lib.rs
@@ -8,7 +8,7 @@
 
 use num_bigint::{BigInt, BigUint};
 use num_integer::Integer;
-use num_traits::{Num, One, Pow, Signed, Zero};
+use num_traits::{Num, One, Signed, Zero};
 use quickcheck::{QuickCheck, StdThreadGen, TestResult};
 use quickcheck_macros::quickcheck;
 
diff --git a/ci/big_rand/src/lib.rs b/ci/big_rand/src/lib.rs
index 8bb19116..2c22db0a 100644
--- a/ci/big_rand/src/lib.rs
+++ b/ci/big_rand/src/lib.rs
@@ -10,7 +10,7 @@ mod torture;
 
 mod biguint {
     use num_bigint::{BigUint, RandBigInt, RandomBits};
-    use num_traits::{Pow, Zero};
+    use num_traits::Zero;
     use rand::distributions::Uniform;
     use rand::thread_rng;
     use rand::{Rng, SeedableRng};
diff --git a/src/bigint.rs b/src/bigint.rs
index 6a405e6a..873983cc 100644
--- a/src/bigint.rs
+++ b/src/bigint.rs
@@ -937,12 +937,30 @@ fn powsign<T: Integer>(sign: Sign, other: &T) -> Sign {
 
 macro_rules! pow_impl {
     ($T:ty) => {
+        impl Pow<$T> for BigInt {
+            type Output = BigInt;
+
+            #[inline]
+            fn pow(self, rhs: $T) -> BigInt {
+                BigInt::from_biguint(powsign(self.sign, &rhs), self.data.pow(rhs))
+            }
+        }
+
+        impl<'b> Pow<&'b $T> for BigInt {
+            type Output = BigInt;
+
+            #[inline]
+            fn pow(self, rhs: &$T) -> BigInt {
+                BigInt::from_biguint(powsign(self.sign, rhs), self.data.pow(rhs))
+            }
+        }
+
         impl<'a> Pow<$T> for &'a BigInt {
             type Output = BigInt;
 
             #[inline]
             fn pow(self, rhs: $T) -> BigInt {
-                BigInt::from_biguint(powsign(self.sign, &rhs), (&self.data).pow(rhs))
+                BigInt::from_biguint(powsign(self.sign, &rhs), Pow::pow(&self.data, rhs))
             }
         }
 
@@ -951,7 +969,7 @@ macro_rules! pow_impl {
 
             #[inline]
             fn pow(self, rhs: &$T) -> BigInt {
-                BigInt::from_biguint(powsign(self.sign, rhs), (&self.data).pow(rhs))
+                BigInt::from_biguint(powsign(self.sign, rhs), Pow::pow(&self.data, rhs))
             }
         }
     };
@@ -3008,6 +3026,11 @@ impl BigInt {
         Some(self.div(v))
     }
 
+    /// Returns `self ^ exponent`.
+    pub fn pow(&self, exponent: u32) -> Self {
+        Pow::pow(self, exponent)
+    }
+
     /// Returns `(self ^ exponent) mod modulus`
     ///
     /// Note that this rounds like `mod_floor`, not like the `%` operator,
diff --git a/src/biguint.rs b/src/biguint.rs
index e71e3e94..532448b9 100644
--- a/src/biguint.rs
+++ b/src/biguint.rs
@@ -547,12 +547,33 @@ impl One for BigUint {
 
 impl Unsigned for BigUint {}
 
-impl<'a> Pow<BigUint> for &'a BigUint {
+impl<'b> Pow<&'b BigUint> for BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn pow(self, exp: &BigUint) -> BigUint {
+        if self.is_one() || exp.is_zero() {
+            BigUint::one()
+        } else if self.is_zero() {
+            BigUint::zero()
+        } else if let Some(exp) = exp.to_u64() {
+            self.pow(exp)
+        } else if let Some(exp) = exp.to_u128() {
+            self.pow(exp)
+        } else {
+            // At this point, `self >= 2` and `exp >= 2¹²⁸`. The smallest possible result given
+            // `2.pow(2¹²⁸)` would require far more memory than 64-bit targets can address!
+            panic!("memory overflow")
+        }
+    }
+}
+
+impl Pow<BigUint> for BigUint {
     type Output = BigUint;
 
     #[inline]
-    fn pow(self, exp: BigUint) -> Self::Output {
-        self.pow(&exp)
+    fn pow(self, exp: BigUint) -> BigUint {
+        Pow::pow(self, &exp)
     }
 }
 
@@ -560,32 +581,36 @@ impl<'a, 'b> Pow<&'b BigUint> for &'a BigUint {
     type Output = BigUint;
 
     #[inline]
-    fn pow(self, exp: &BigUint) -> Self::Output {
+    fn pow(self, exp: &BigUint) -> BigUint {
         if self.is_one() || exp.is_zero() {
             BigUint::one()
         } else if self.is_zero() {
             BigUint::zero()
-        } else if let Some(exp) = exp.to_u64() {
-            self.pow(exp)
         } else {
-            // At this point, `self >= 2` and `exp >= 2⁶⁴`.  The smallest possible result
-            // given `2.pow(2⁶⁴)` would take 2.3 exabytes of memory!
-            panic!("memory overflow")
+            self.clone().pow(exp)
         }
     }
 }
 
+impl<'a> Pow<BigUint> for &'a BigUint {
+    type Output = BigUint;
+
+    #[inline]
+    fn pow(self, exp: BigUint) -> BigUint {
+        Pow::pow(self, &exp)
+    }
+}
+
 macro_rules! pow_impl {
     ($T:ty) => {
-        impl<'a> Pow<$T> for &'a BigUint {
+        impl Pow<$T> for BigUint {
             type Output = BigUint;
 
-            #[inline]
-            fn pow(self, mut exp: $T) -> Self::Output {
+            fn pow(self, mut exp: $T) -> BigUint {
                 if exp == 0 {
                     return BigUint::one();
                 }
-                let mut base = self.clone();
+                let mut base = self;
 
                 while exp & 1 == 0 {
                     base = &base * &base;
@@ -608,12 +633,33 @@ macro_rules! pow_impl {
             }
         }
 
+        impl<'b> Pow<&'b $T> for BigUint {
+            type Output = BigUint;
+
+            #[inline]
+            fn pow(self, exp: &$T) -> BigUint {
+                Pow::pow(self, *exp)
+            }
+        }
+
+        impl<'a> Pow<$T> for &'a BigUint {
+            type Output = BigUint;
+
+            #[inline]
+            fn pow(self, exp: $T) -> BigUint {
+                if exp == 0 {
+                    return BigUint::one();
+                }
+                Pow::pow(self.clone(), exp)
+            }
+        }
+
         impl<'a, 'b> Pow<&'b $T> for &'a BigUint {
             type Output = BigUint;
 
             #[inline]
-            fn pow(self, exp: &$T) -> Self::Output {
-                self.pow(*exp)
+            fn pow(self, exp: &$T) -> BigUint {
+                Pow::pow(self, *exp)
             }
         }
     };
@@ -2504,6 +2550,11 @@ impl BigUint {
         self
     }
 
+    /// Returns `self ^ exponent`.
+    pub fn pow(&self, exponent: u32) -> Self {
+        Pow::pow(self, exponent)
+    }
+
     /// Returns `(self ^ exponent) % modulus`.
     ///
     /// Panics if the modulus is zero.
@@ -2614,7 +2665,7 @@ fn plain_modpow(base: &BigUint, exp_data: &[BigDigit], modulus: &BigUint) -> Big
 
 #[test]
 fn test_plain_modpow() {
-    let two = BigUint::from(2u32);
+    let two = &BigUint::from(2u32);
     let modulus = BigUint::from(0x1100u32);
 
     let exp = vec![0, 0b1];
diff --git a/tests/bigint.rs b/tests/bigint.rs
index 1a130611..e649dc18 100644
--- a/tests/bigint.rs
+++ b/tests/bigint.rs
@@ -1148,15 +1148,15 @@ fn test_pow() {
     let minus_two = BigInt::from(-2i32);
     macro_rules! check {
         ($t:ty) => {
-            assert_eq!(two.pow(0 as $t), one);
-            assert_eq!(two.pow(1 as $t), two);
-            assert_eq!(two.pow(2 as $t), four);
-            assert_eq!(two.pow(3 as $t), eight);
-            assert_eq!(two.pow(&(3 as $t)), eight);
-            assert_eq!(minus_two.pow(0 as $t), one, "-2^0");
-            assert_eq!(minus_two.pow(1 as $t), minus_two, "-2^1");
-            assert_eq!(minus_two.pow(2 as $t), four, "-2^2");
-            assert_eq!(minus_two.pow(3 as $t), -&eight, "-2^3");
+            assert_eq!(Pow::pow(&two, 0 as $t), one);
+            assert_eq!(Pow::pow(&two, 1 as $t), two);
+            assert_eq!(Pow::pow(&two, 2 as $t), four);
+            assert_eq!(Pow::pow(&two, 3 as $t), eight);
+            assert_eq!(Pow::pow(&two, &(3 as $t)), eight);
+            assert_eq!(Pow::pow(&minus_two, 0 as $t), one, "-2^0");
+            assert_eq!(Pow::pow(&minus_two, 1 as $t), minus_two, "-2^1");
+            assert_eq!(Pow::pow(&minus_two, 2 as $t), four, "-2^2");
+            assert_eq!(Pow::pow(&minus_two, 3 as $t), -&eight, "-2^3");
         };
     }
     check!(u8);
diff --git a/tests/biguint.rs b/tests/biguint.rs
index cd944f97..7f99eb4f 100644
--- a/tests/biguint.rs
+++ b/tests/biguint.rs
@@ -1676,13 +1676,13 @@ fn test_pow() {
     let twentyfourtyeight = BigUint::from(2048u32);
     macro_rules! check {
         ($t:ty) => {
-            assert_eq!(two.pow(0 as $t), one);
-            assert_eq!(two.pow(1 as $t), two);
-            assert_eq!(two.pow(2 as $t), four);
-            assert_eq!(two.pow(3 as $t), eight);
-            assert_eq!(two.pow(10 as $t), tentwentyfour);
-            assert_eq!(two.pow(11 as $t), twentyfourtyeight);
-            assert_eq!(two.pow(&(11 as $t)), twentyfourtyeight);
+            assert_eq!(Pow::pow(&two, 0 as $t), one);
+            assert_eq!(Pow::pow(&two, 1 as $t), two);
+            assert_eq!(Pow::pow(&two, 2 as $t), four);
+            assert_eq!(Pow::pow(&two, 3 as $t), eight);
+            assert_eq!(Pow::pow(&two, 10 as $t), tentwentyfour);
+            assert_eq!(Pow::pow(&two, 11 as $t), twentyfourtyeight);
+            assert_eq!(Pow::pow(&two, &(11 as $t)), twentyfourtyeight);
         };
     }
     check!(u8);
diff --git a/tests/roots.rs b/tests/roots.rs
index fdd609d2..cfef80c4 100644
--- a/tests/roots.rs
+++ b/tests/roots.rs
@@ -1,6 +1,6 @@
 mod biguint {
     use num_bigint::BigUint;
-    use num_traits::{One, Pow, Zero};
+    use num_traits::{One, Zero};
     use std::{i32, u32};
 
     fn check<T: Into<BigUint>>(x: T, n: u32) {
@@ -114,7 +114,7 @@ mod biguint {
 
 mod bigint {
     use num_bigint::BigInt;
-    use num_traits::{Pow, Signed};
+    use num_traits::Signed;
 
     fn check(x: i64, n: u32) {
         let big_x = BigInt::from(x);