diff --git a/poincare/src/power.cpp b/poincare/src/power.cpp
index a57c0918e..ec1c0bcac 100644
--- a/poincare/src/power.cpp
+++ b/poincare/src/power.cpp
@@ -5,6 +5,7 @@
 #include <poincare/constant.h>
 #include <poincare/cosine.h>
 #include <poincare/division.h>
+#include <poincare/infinity.h>
 #include <poincare/nth_root.h>
 #include <poincare/opposite.h>
 #include <poincare/parenthesis.h>
@@ -386,6 +387,29 @@ Expression Power::shallowReduce(Context & context, Preferences::AngleUnit angleU
       return result.shallowReduce(context, angleUnit);
     }
   }
+
+  // (±inf)^x
+  if (childAtIndex(0).type() == ExpressionNode::Type::Infinity) {
+    Expression result;
+    if (childAtIndex(1).sign() == ExpressionNode::Sign::Negative) {
+      // --> 0 if x < 0
+      result = Rational(0);
+    } else if (childAtIndex(1).sign() == ExpressionNode::Sign::Positive) {
+      // --> (±inf) if x > 0
+      result = Infinity(false);
+      if (childAtIndex(0).sign() == ExpressionNode::Sign::Negative) {
+        // (-inf)^x --> (-1)^x*inf
+        Power p(Rational(-1), childAtIndex(1));
+        result = Multiplication(p, result);
+        p.shallowReduce(context, angleUnit);
+      }
+    }
+    if (!result.isUninitialized()) {
+      replaceWithInPlace(result);
+      return result.shallowReduce(context, angleUnit);
+    }
+  }
+
   bool letPowerAtRoot = parentIsALogarithmOfSameBase();
   if (childAtIndex(0).type() == ExpressionNode::Type::Rational) {
     Rational a = childAtIndex(0).convert<Rational>();
diff --git a/poincare/test/infinity.cpp b/poincare/test/infinity.cpp
index 1fe7e408b..aff3038ba 100644
--- a/poincare/test/infinity.cpp
+++ b/poincare/test/infinity.cpp
@@ -17,10 +17,22 @@ QUIZ_CASE(poincare_infinity) {
   assert_parsed_expression_simplify_to("0/inf", "0");
   assert_parsed_expression_simplify_to("inf/0", Undefined::Name());
   assert_parsed_expression_simplify_to("0*inf", Undefined::Name());
-  assert_parsed_expression_simplify_to("3*inf/inf", "inf/inf"); //TODO undef would be better
+  assert_parsed_expression_simplify_to("3*inf/inf", "undef");
   assert_parsed_expression_simplify_to("1E1000", "inf");
   assert_parsed_expression_simplify_to("-1E1000", "-inf");
   assert_parsed_expression_simplify_to("-1E-1000", "0");
   assert_parsed_expression_simplify_to("1E-1000", "0");
   assert_parsed_expression_evaluates_to<double>("1*10^1000", "inf");
+
+  assert_parsed_expression_simplify_to("inf^(-1)", "0");
+  assert_parsed_expression_simplify_to("(-inf)^(-1)", "0");
+  assert_parsed_expression_simplify_to("inf^(-R(2))", "0");
+  assert_parsed_expression_simplify_to("(-inf)^(-R(2))", "0");
+  assert_parsed_expression_simplify_to("inf^2", "inf");
+  assert_parsed_expression_simplify_to("(-inf)^2", "inf");
+  assert_parsed_expression_simplify_to("inf^R(2)", "inf");
+  assert_parsed_expression_simplify_to("(-inf)^R(2)", "inf*(-1)^R(2)");
+  assert_parsed_expression_simplify_to("inf^x", "inf^x");
+  assert_parsed_expression_simplify_to("1/inf+24", "24");
+
 }
diff --git a/poincare/test/rational.cpp b/poincare/test/rational.cpp
index 2df36c9ee..b8d740a36 100644
--- a/poincare/test/rational.cpp
+++ b/poincare/test/rational.cpp
@@ -89,7 +89,7 @@ QUIZ_CASE(poincare_rational_simplify) {
   assert_parsed_expression_simplify_to(buffer, buffer);
   // 1/OverflowedIntegerString()
   strlcpy(buffer+2, BigOverflowedIntegerString(), 400-2);
-  assert_parsed_expression_simplify_to(buffer, "1/inf");
+  assert_parsed_expression_simplify_to(buffer, "0");
   // MaxIntegerString()
   assert_parsed_expression_simplify_to(MaxIntegerString(), MaxIntegerString());
   // OverflowedIntegerString()