diff --git a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
index 21b097609..749cd5e75 100644
--- a/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
+++ b/benchmarks/src/jvmMain/kotlin/space/kscience/kmath/benchmarks/BigIntBenchmark.kt
@@ -21,7 +21,7 @@ internal class BigIntBenchmark {
 
     val kmNumber = BigIntField.number(Int.MAX_VALUE)
     val jvmNumber = JBigIntegerField.number(Int.MAX_VALUE)
-    val largeKmNumber = BigIntField { number(11).pow(100_000UL) }
+    val largeKmNumber = BigIntField { number(11).pow(100_000U) }
     val largeJvmNumber: BigInteger = JBigIntegerField { number(11).pow(100_000) }
     val bigExponent = 50_000
 
@@ -67,7 +67,7 @@ internal class BigIntBenchmark {
 
     @Benchmark
     fun kmPower(blackhole: Blackhole) = BigIntField {
-        blackhole.consume(kmNumber.pow(bigExponent.toULong()))
+        blackhole.consume(kmNumber.pow(bigExponent.toUInt()))
     }
 
     @Benchmark
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
index 8881ae93c..b444ed964 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/Algebra.kt
@@ -253,26 +253,6 @@ public interface Ring<T> : Group<T>, RingOperations<T> {
     public val one: T
 }
 
-@UnstableKMathAPI
-public fun <T> Ring<T>.pow(base: T, exponent: ULong): T = when {
-    this == zero && exponent > 0UL -> zero
-    this == one -> base
-    this == -one -> powWithoutOptimization(base, exponent % 2UL)
-    else -> powWithoutOptimization(base, exponent)
-}
-
-@UnstableKMathAPI
-public fun <T> Ring<T>.pow(base: T, exponent: UInt): T = pow(base, exponent.toULong())
-
-private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: ULong): T = when (exponent) {
-    0UL -> one
-    1UL -> base
-    else -> {
-        val pre = powWithoutOptimization(base, exponent shr 1).let { it * it }
-        if (exponent and 1UL == 0UL) pre else pre * base
-    }
-}
-
 /**
  * Represents field without without multiplicative and additive identities, i.e. algebraic structure with associative, binary, commutative operations
  * [add] and [multiply]; binary operation [divide] as multiplication of left operand by reciprocal of right one.
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
index 0dcbbe567..924ef07f4 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/BigInt.kt
@@ -98,11 +98,7 @@ public class BigInt internal constructor(
         else -> BigInt(sign, multiplyMagnitudeByUInt(magnitude, other))
     }
 
-    @UnstableKMathAPI
-    public fun pow(other: ULong): BigInt = BigIntField { pow(this@BigInt, other) }
-
-    @UnstableKMathAPI
-    public fun pow(other: UInt): BigInt = BigIntField { pow(this@BigInt, other) }
+    public fun pow(exponent: UInt): BigInt = BigIntField.power(this@BigInt, exponent)
 
     public operator fun times(other: Int): BigInt = when {
         other > 0 -> this * kotlin.math.abs(other).toUInt()
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
index b8670553d..9691c9d17 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/operations/algebraExtensions.kt
@@ -97,34 +97,45 @@ public fun <T, S> Sequence<T>.averageWith(space: S): T where S : Ring<T>, S : Sc
 //TODO optimized power operation
 
 /**
- * Raises [arg] to the natural power [power].
+ * Raises [arg] to the non-negative integer power [power].
+ *
+ * Special case: 0 ^ 0 is 1.
  *
  * @receiver the algebra to provide multiplication.
  * @param arg the base.
  * @param power the exponent.
  * @return the base raised to the power.
+ * @author Evgeniy Zhelenskiy
  */
-public fun <T> Ring<T>.power(arg: T, power: Int): T {
-    require(power >= 0) { "The power can't be negative." }
-    require(power != 0 || arg != zero) { "The $zero raised to $power is not defined." }
-    if (power == 0) return one
-    var res = arg
-    repeat(power - 1) { res *= arg }
-    return res
+public fun <T> Ring<T>.power(arg: T, power: UInt): T = when {
+    this == zero && power > 0U -> zero
+    this == one -> arg
+    this == -one -> powWithoutOptimization(arg, power % 2U)
+    else -> powWithoutOptimization(arg, power)
 }
 
+private fun <T> Ring<T>.powWithoutOptimization(base: T, exponent: UInt): T = when (exponent) {
+    0U -> one
+    1U -> base
+    else -> {
+        val pre = powWithoutOptimization(base, exponent shr 1).let { it * it }
+        if (exponent and 1U == 0U) pre else pre * base
+    }
+}
+
+
 /**
  * Raises [arg] to the integer power [power].
  *
+ * Special case: 0 ^ 0 is 1.
+ *
  * @receiver the algebra to provide multiplication and division.
  * @param arg the base.
  * @param power the exponent.
  * @return the base raised to the power.
- * @author Iaroslav Postovalov
+ * @author Iaroslav Postovalov, Evgeniy Zhelenskiy
  */
-public fun <T> Field<T>.power(arg: T, power: Int): T {
-    require(power != 0 || arg != zero) { "The $zero raised to $power is not defined." }
-    if (power == 0) return one
-    if (power < 0) return one / (this as Ring<T>).power(arg, -power)
-    return (this as Ring<T>).power(arg, power)
+public fun <T> Field<T>.power(arg: T, power: Int): T = when {
+    power < 0 -> one / (this as Ring<T>).power(arg, if (power == Int.MIN_VALUE) Int.MAX_VALUE.toUInt().inc() else (-power).toUInt())
+    else -> (this as Ring<T>).power(arg, power.toUInt())
 }
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
index d3fca4351..0527f5252 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/BigIntAlgebraTest.kt
@@ -27,18 +27,12 @@ internal class BigIntAlgebraTest {
     @Test
     fun testKBigIntegerRingPow() {
         for (num in -5..5)
-            for (exponent in 0U..10U) {
-                assertEquals(
-                    num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
-                    num.toBigInt().pow(exponent.toULong()),
-                    "$num ^ $exponent"
-                )
+            for (exponent in 0U..10U)
                 assertEquals(
                     num.toDouble().pow(exponent.toInt()).toLong().toBigInt(),
                     num.toBigInt().pow(exponent),
                     "$num ^ $exponent"
                 )
-            }
     }
 
     @Test
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt
index c482dc978..7e689d079 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/operations/DoubleFieldTest.kt
@@ -18,4 +18,16 @@ internal class DoubleFieldTest {
         val sqrt = DoubleField { sqrt(25 * one) }
         assertEquals(5.0, sqrt)
     }
+
+    @Test
+    fun testPow() = DoubleField {
+        val num = 5 * one
+        assertEquals(5.0, power(num, 1))
+        assertEquals(25.0, power(num, 2))
+        assertEquals(1.0, power(num, 0))
+        assertEquals(0.2, power(num, -1))
+        assertEquals(0.04, power(num, -2))
+        assertEquals(0.0, power(num, Int.MIN_VALUE))
+        assertEquals(1.0, power(zero, 0))
+    }
 }