diff --git a/.Rbuildignore b/.Rbuildignore
index a6a8b1e..6da8a56 100644
--- a/.Rbuildignore
+++ b/.Rbuildignore
@@ -7,3 +7,5 @@
 README.md
 ^quantities$
 ^revdep$
+^\.positai$
+^\.claude$
diff --git a/.gitignore b/.gitignore
index 28b2a66..0366d92 100644
--- a/.gitignore
+++ b/.gitignore
@@ -37,3 +37,4 @@ configure.scan
 # OSX-specific
 .DS_Store
 inst/doc
+.positai
diff --git a/DESCRIPTION b/DESCRIPTION
index e977c5a..115332c 100644
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,5 +1,5 @@
 Package: units
-Version: 1.0-1.3
+Version: 1.0-1.4
 Title: Measurement Units for R Vectors
 Authors@R: c(person("Edzer", "Pebesma", role = c("aut", "cre"), email = "edzer.pebesma@uni-muenster.de", comment = c(ORCID = "0000-0001-8049-7069")),
     person("Thomas", "Mailund", role = "aut", email = "mailund@birc.au.dk"),
diff --git a/NEWS.md b/NEWS.md
index ef873ad..1dc2f5e 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -6,6 +6,8 @@
 
 * Several fixes in documentation files; #433 @tszberkowitz
 
+* Simplify unitless powers automatically; #435 addressing #179, #434
+
 # version 1.0-1
 
 * Add internal workaround for udunits2 bug with parsing of units that contain
diff --git a/R/arith.R b/R/arith.R
index 8d5cb79..0751200 100644
--- a/R/arith.R
+++ b/R/arith.R
@@ -128,12 +128,14 @@ Ops.units <- function(e1, e2) {
     return(.simplify_units(NextMethod(), .symbolic_units(numerator, denominator)))
 
   } else if (pw) {
-    if (e2_inherits_units) {
-      if (e1_inherits_units && identical(units(e1), units(as_units(1)))) {
+    if (e2_inherits_units && identical(units(e2), unitless)) {
+      e2 <- drop_units(e2)
+      if (!e1_inherits_units)
+        return(NextMethod())
+
+    } else if (e2_inherits_units) {
+      if (e1_inherits_units && identical(units(e1), unitless))
         e1 <- drop_units(e1)
-      } else if (e1_inherits_units) {
-        stop("power operation only allowed with numeric power")
-      }
 
       # code to manage things like exp(log(...)) and 10^log10(...) follows
       # this is not supported in udunits2, so we are on our own
@@ -179,7 +181,7 @@ Ops.units <- function(e1, e2) {
     # when the power is negative and we have a special case when it is zero where
     # units should be removed.
     if (e2 == 0) {
-      u <- units(as_units(1))
+      u <- unitless
     } else {
       tbl_den <- tabulate(factor(units(e1)$denominator))
       tbl_num <- tabulate(factor(units(e1)$numerator))
diff --git a/tests/testthat/test_arith.R b/tests/testthat/test_arith.R
index 3105f67..e70db59 100644
--- a/tests/testthat/test_arith.R
+++ b/tests/testthat/test_arith.R
@@ -91,8 +91,8 @@ test_that("we can take powers of units", {
 
   expect_equal(as.numeric(ux ** 0), x ** 0)
   expect_equal(as.numeric(ux ^ 0), x ^ 0)
-  expect_identical(units(ux ** 0), units(as_units(1)))
-  expect_identical(units(ux ^ 0), units(as_units(1)))
+  expect_identical(units(ux ** 0), unitless)
+  expect_identical(units(ux ^ 0), unitless)
 })
 
 test_that("we support unary +/-", {
@@ -181,7 +181,7 @@ test_that("we can undo logatithms", {
   expect_equal(expm1(3^log(log1p(y), base=3)), set_units(y, m^2))
   expect_error(exp(log10(x)), "wrong base in power operation")
   expect_error(exp(x), "only allowed with logarithmic unit")
-  expect_error(exp(set_units(1, 1)), "only allowed with logarithmic unit")
+  expect_equal(exp(x/y), exp(drop_units(x/y)))
 })
 
 test_that("%/% and %% work", {