Precedence is a property of notation and operators, not a property of operations. The ^ notation for exponentiation is fundamentally different from the common s

Precedence is a property of notation and operators, not a property of operations. The ^ notation for exponentiation is fundamentally different from the common superscript notation, and so it is only natural that it has different precedence rule. The biggest difference is in how exponent expressions are handled, of course: in math notation, the entire expression is written in superscript and no parantheses are needed; in computer notation, you always need parantheses around the exponent expression.