diff --git a/cpp/src/arrow/compute/api_scalar.cc b/cpp/src/arrow/compute/api_scalar.cc
index f4696fbe02a..d169fd2ebde 100644
--- a/cpp/src/arrow/compute/api_scalar.cc
+++ b/cpp/src/arrow/compute/api_scalar.cc
@@ -52,6 +52,7 @@ SCALAR_ARITHMETIC_BINARY(Add, "add", "add_checked")
 SCALAR_ARITHMETIC_BINARY(Subtract, "subtract", "subtract_checked")
 SCALAR_ARITHMETIC_BINARY(Multiply, "multiply", "multiply_checked")
 SCALAR_ARITHMETIC_BINARY(Divide, "divide", "divide_checked")
+SCALAR_ARITHMETIC_BINARY(Power, "power", "power_checked")
 
 // ----------------------------------------------------------------------
 // Set-related operations
diff --git a/cpp/src/arrow/compute/api_scalar.h b/cpp/src/arrow/compute/api_scalar.h
index f59426d8f1b..6032f656c4a 100644
--- a/cpp/src/arrow/compute/api_scalar.h
+++ b/cpp/src/arrow/compute/api_scalar.h
@@ -204,6 +204,20 @@ Result<Datum> Divide(const Datum& left, const Datum& right,
                      ArithmeticOptions options = ArithmeticOptions(),
                      ExecContext* ctx = NULLPTR);
 
+/// \brief Raise the values of base array to the power of the exponent array values.
+/// Array values must be the same length. If either base or exponent is null the result
+/// will be null.
+///
+/// \param[in] left the base
+/// \param[in] right the exponent
+/// \param[in] options arithmetic options (enable/disable overflow checking), optional
+/// \param[in] ctx the function execution context, optional
+/// \return the elementwise base value raised to the power of exponent
+ARROW_EXPORT
+Result<Datum> Power(const Datum& left, const Datum& right,
+                    ArithmeticOptions options = ArithmeticOptions(),
+                    ExecContext* ctx = NULLPTR);
+
 /// \brief Compare a numeric array with a scalar.
 ///
 /// \param[in] left datum to compare, must be an Array
diff --git a/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc b/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc
index 7abaa1c1a59..260721b08d9 100644
--- a/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_arithmetic.cc
@@ -15,6 +15,8 @@
 // specific language governing permissions and limitations
 // under the License.
 
+#include <cmath>
+
 #include "arrow/compute/kernels/common.h"
 #include "arrow/util/int_util_internal.h"
 #include "arrow/util/macros.h"
@@ -233,6 +235,70 @@ struct DivideChecked {
   }
 };
 
+struct Power {
+  ARROW_NOINLINE
+  static uint64_t IntegerPower(uint64_t base, uint64_t exp) {
+    // right to left O(logn) power
+    uint64_t pow = 1;
+    while (exp) {
+      pow *= (exp & 1) ? base : 1;
+      base *= base;
+      exp >>= 1;
+    }
+    return pow;
+  }
+
+  template <typename T>
+  static enable_if_integer<T> Call(KernelContext* ctx, T base, T exp) {
+    if (exp < 0) {
+      ctx->SetStatus(
+          Status::Invalid("integers to negative integer powers are not allowed"));
+      return 0;
+    }
+    return static_cast<T>(IntegerPower(base, exp));
+  }
+
+  template <typename T>
+  static enable_if_floating_point<T> Call(KernelContext* ctx, T base, T exp) {
+    return std::pow(base, exp);
+  }
+};
+
+struct PowerChecked {
+  template <typename T, typename Arg0, typename Arg1>
+  static enable_if_integer<T> Call(KernelContext* ctx, Arg0 base, Arg1 exp) {
+    if (exp < 0) {
+      ctx->SetStatus(
+          Status::Invalid("integers to negative integer powers are not allowed"));
+      return 0;
+    } else if (exp == 0) {
+      return 1;
+    }
+    // left to right O(logn) power with overflow checks
+    bool overflow = false;
+    uint64_t bitmask =
+        1ULL << (63 - BitUtil::CountLeadingZeros(static_cast<uint64_t>(exp)));
+    T pow = 1;
+    while (bitmask) {
+      overflow |= MultiplyWithOverflow(pow, pow, &pow);
+      if (exp & bitmask) {
+        overflow |= MultiplyWithOverflow(pow, base, &pow);
+      }
+      bitmask >>= 1;
+    }
+    if (overflow) {
+      ctx->SetStatus(Status::Invalid("overflow"));
+    }
+    return pow;
+  }
+
+  template <typename T, typename Arg0, typename Arg1>
+  static enable_if_floating_point<T> Call(KernelContext* ctx, Arg0 base, Arg1 exp) {
+    static_assert(std::is_same<T, Arg0>::value && std::is_same<T, Arg1>::value, "");
+    return std::pow(base, exp);
+  }
+};
+
 // Generate a kernel given an arithmetic functor
 template <template <typename... Args> class KernelGenerator, typename Op>
 ArrayKernelExec NumericEqualTypesBinary(detail::GetTypeId get_id) {
@@ -359,6 +425,18 @@ const FunctionDoc div_checked_doc{
      "integer overflow is encountered."),
     {"dividend", "divisor"}};
 
+const FunctionDoc pow_doc{
+    "Raise arguments to power element-wise",
+    ("Integer to negative integer power returns an error. However, integer overflow\n"
+     "wraps around. If either base or exponent is null the result will be null."),
+    {"base", "exponent"}};
+
+const FunctionDoc pow_checked_doc{
+    "Raise arguments to power element-wise",
+    ("An error is returned when integer to negative integer power is encountered,\n"
+     "or integer overflow is encountered."),
+    {"base", "exponent"}};
+
 }  // namespace
 
 void RegisterScalarArithmetic(FunctionRegistry* registry) {
@@ -407,6 +485,15 @@ void RegisterScalarArithmetic(FunctionRegistry* registry) {
   auto divide_checked =
       MakeArithmeticFunctionNotNull<DivideChecked>("divide_checked", &div_checked_doc);
   DCHECK_OK(registry->AddFunction(std::move(divide_checked)));
+
+  // ----------------------------------------------------------------------
+  auto power = MakeArithmeticFunction<Power>("power", &pow_doc);
+  DCHECK_OK(registry->AddFunction(std::move(power)));
+
+  // ----------------------------------------------------------------------
+  auto power_checked =
+      MakeArithmeticFunctionNotNull<PowerChecked>("power_checked", &pow_checked_doc);
+  DCHECK_OK(registry->AddFunction(std::move(power_checked)));
 }
 
 }  // namespace internal
diff --git a/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc b/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc
index 4d4f14e1154..cd5f298ae51 100644
--- a/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc
+++ b/cpp/src/arrow/compute/kernels/scalar_arithmetic_test.cc
@@ -590,6 +590,114 @@ TYPED_TEST(TestBinaryArithmeticSigned, DivideOverflowRaises) {
   this->AssertBinop(Divide, MakeArray(min), MakeArray(-1), "[0]");
 }
 
+TYPED_TEST(TestBinaryArithmeticFloating, Power) {
+  using CType = typename TestFixture::CType;
+  auto max = std::numeric_limits<CType>::max();
+  this->SetNansEqual(true);
+
+  for (auto check_overflow : {false, true}) {
+    this->SetOverflowCheck(check_overflow);
+
+    // Empty arrays
+    this->AssertBinop(Power, "[]", "[]", "[]");
+    // Ordinary arrays
+    this->AssertBinop(Power, "[3.4, 16, 0.64, 1.2, 0]", "[1, 0.5, 2, 4, 0]",
+                      "[3.4, 4, 0.4096, 2.0736, 1]");
+    // Array with nulls
+    this->AssertBinop(Power, "[null, 1, 3.3, null, 2]", "[1, 4, 2, 5, 0.1]",
+                      "[null, 1, 10.89, null, 1.07177346]");
+    // Scalar exponentiated by array
+    this->AssertBinop(Power, 10.0F, "[null, 1, 2.5, null, 2, 5]",
+                      "[null, 10, 316.227766017, null, 100, 100000]");
+    // Array exponentiated by scalar
+    this->AssertBinop(Power, "[null, 1, 2.5, null, 2, 5]", 10.0F,
+                      "[null, 1, 9536.74316406, null, 1024, 9765625]");
+    // Array with infinity
+    this->AssertBinop(Power, "[3.4, Inf, -Inf, 1.1, 100000]", "[1, 2, 3, Inf, 100000]",
+                      "[3.4, Inf, -Inf, Inf, Inf]");
+    // Array with NaN
+    this->AssertBinop(Power, "[3.4, NaN, 2.0]", "[1, 2, 2.0]", "[3.4, NaN, 4.0]");
+    // Scalar exponentiated by scalar
+    this->AssertBinop(Power, 21.0F, 3.0F, 9261.0F);
+    // Divide by zero
+    this->AssertBinop(Power, "[0.0, 0.0]", "[-1.0, -3.0]", "[Inf, Inf]");
+    // Check overflow behaviour
+    this->AssertBinop(Power, max, 10, INFINITY);
+  }
+
+  // Edge cases - removing NaNs
+  this->AssertBinop(Power, "[1, NaN, 0, null, 1.2, -Inf, Inf, 1.1, 1, 0, 1, 0]",
+                    "[NaN, 0, NaN, 1, null, 1, 2, -Inf, Inf, 0, 0, 42]",
+                    "[1, 1, NaN, null, null, -Inf, Inf, 0, 1, 1, 1, 0]");
+}
+
+TYPED_TEST(TestBinaryArithmeticIntegral, Power) {
+  using CType = typename TestFixture::CType;
+  auto max = std::numeric_limits<CType>::max();
+
+  for (auto check_overflow : {false, true}) {
+    this->SetOverflowCheck(check_overflow);
+
+    // Empty arrays
+    this->AssertBinop(Power, "[]", "[]", "[]");
+    // Ordinary arrays
+    this->AssertBinop(Power, "[3, 2, 6, 2]", "[1, 1, 2, 0]", "[3, 2, 36, 1]");
+    // Array with nulls
+    this->AssertBinop(Power, "[null, 2, 3, null, 20]", "[1, 6, 2, 5, 1]",
+                      "[null, 64, 9, null, 20]");
+    // Scalar exponentiated by array
+    this->AssertBinop(Power, 3, "[null, 3, 4, null, 2]", "[null, 27, 81, null, 9]");
+    // Array exponentiated by scalar
+    this->AssertBinop(Power, "[null, 10, 3, null, 2]", 2, "[null, 100, 9, null, 4]");
+    // Scalar exponentiated by scalar
+    this->AssertBinop(Power, 4, 3, 64);
+    // Edge cases
+    this->AssertBinop(Power, "[0, 1, 0]", "[0, 0, 42]", "[1, 1, 0]");
+  }
+
+  // Overflow raises
+  this->SetOverflowCheck(true);
+  this->AssertBinopRaises(Power, MakeArray(max), MakeArray(10), "overflow");
+  // Disable overflow check
+  this->SetOverflowCheck(false);
+  this->AssertBinop(Power, max, 10, 1);
+}
+
+TYPED_TEST(TestBinaryArithmeticSigned, Power) {
+  using CType = typename TestFixture::CType;
+  auto max = std::numeric_limits<CType>::max();
+
+  for (auto check_overflow : {false, true}) {
+    this->SetOverflowCheck(check_overflow);
+
+    // Empty arrays
+    this->AssertBinop(Power, "[]", "[]", "[]");
+    // Ordinary arrays
+    this->AssertBinop(Power, "[-3, 2, -6, 2]", "[3, 1, 2, 0]", "[-27, 2, 36, 1]");
+    // Array with nulls
+    this->AssertBinop(Power, "[null, 10, 127, null, -20]", "[1, 2, 1, 5, 1]",
+                      "[null, 100, 127, null, -20]");
+    // Scalar exponentiated by array
+    this->AssertBinop(Power, 11, "[null, 1, null, 2]", "[null, 11, null, 121]");
+    // Array exponentiated by scalar
+    this->AssertBinop(Power, "[null, 1, 3, null, 2]", 3, "[null, 1, 27, null, 8]");
+    // Scalar exponentiated by scalar
+    this->AssertBinop(Power, 16, 1, 16);
+    // Edge cases
+    this->AssertBinop(Power, "[1, 0, -1, 2]", "[0, 42, 0, 1]", "[1, 0, 1, 2]");
+    // Divide by zero raises
+    this->AssertBinopRaises(Power, MakeArray(0), MakeArray(-1),
+                            "integers to negative integer powers are not allowed");
+  }
+
+  // Overflow raises
+  this->SetOverflowCheck(true);
+  this->AssertBinopRaises(Power, MakeArray(max), MakeArray(10), "overflow");
+  // Disable overflow check
+  this->SetOverflowCheck(false);
+  this->AssertBinop(Power, max, 10, 1);
+}
+
 TYPED_TEST(TestBinaryArithmeticFloating, Sub) {
   this->AssertBinop(Subtract, "[]", "[]", "[]");
 
@@ -638,7 +746,7 @@ TYPED_TEST(TestBinaryArithmeticFloating, Mul) {
 }
 
 TEST(TestBinaryArithmetic, DispatchBest) {
-  for (std::string name : {"add", "subtract", "multiply", "divide"}) {
+  for (std::string name : {"add", "subtract", "multiply", "divide", "power"}) {
     for (std::string suffix : {"", "_checked"}) {
       name += suffix;
 
diff --git a/docs/source/cpp/compute.rst b/docs/source/cpp/compute.rst
index 715d5036964..b2ecb3b2ceb 100644
--- a/docs/source/cpp/compute.rst
+++ b/docs/source/cpp/compute.rst
@@ -272,6 +272,10 @@ an ``Invalid`` :class:`Status` when overflow is detected.
 +--------------------------+------------+--------------------+---------------------+
 | divide_checked           | Binary     | Numeric            | Numeric             |
 +--------------------------+------------+--------------------+---------------------+
+| power                    | Binary     | Numeric            | Numeric             |
++--------------------------+------------+--------------------+---------------------+
+| power_checked            | Binary     | Numeric            | Numeric             |
++--------------------------+------------+--------------------+---------------------+
 | multiply                 | Binary     | Numeric            | Numeric             |
 +--------------------------+------------+--------------------+---------------------+
 | multiply_checked         | Binary     | Numeric            | Numeric             |
diff --git a/docs/source/python/api/compute.rst b/docs/source/python/api/compute.rst
index d6efc6a5fea..da16ccdfa29 100644
--- a/docs/source/python/api/compute.rst
+++ b/docs/source/python/api/compute.rst
@@ -53,6 +53,8 @@ throws an ``ArrowInvalid`` exception when overflow is detected.
    multiply_checked
    subtract
    subtract_checked
+   power
+   power_checked
 
 Comparisons
 -----------