The idea of operator precedence - also known as order of operations - is a relatively recent concept, in part because the common mathematical operators for the four basic arithmetical operations - $+,-,\times,\div$ - weren't all in use until a few hundred years ago. For example, as Florian Cajori writes in A History of Mathematics, one of the symbols for multiplication ($\times$) was created by William Oughtred in the 17th century. This means that older cultures didn't have the same system we use today.
That said, according to this source,
The convention that multiplication precedes addition and subtraction was in use in the earliest books employing symbolic algebra in the 16th century. The convention that exponentiation precedes multiplication was used in the earliest books in which exponents appeared.
The debate about the order of multiplication/division came later, although given that the two operations are inverses of each other, it is not as important.