title: Operator precedence 'pow' and 'root'
body: <p>I am writing a little home-made calculator for integers and it includes two binary operators, 'pow' and 'root'. The 'pow' operator evaluates (left operand) ^ (right operand), and the 'root' operator finds the largest number n such that n ^ (left operand) &lt;= (right operand).</p>
  
  <p>Assuming this isn't an absurd thing to do, what should the precedence of these operators be? Currently I have them at equal precedence so strings such as</p>
  
  <pre><code>3 root 1500 pow 7
  </code></pre>
  
  <p>evaluate left to right. Is this right? Should I put this question on mathoverflow?</p>