What's the general form for $x^y$? What's the specialized form for $x^1$ and $x^0$?
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As J.M. and Rahul Narain pointed out in comments, $x^1$ is often referred to as "linear" and $x^0$ as "constant." Commonly, though certainly not universally, $x^y$ is a/the "power" with $x$ as the base and $y$ as the exponent.
$x$ used to be called latus (latin for side---of a square, a cube)
If you are interested in this, you must read Cajori's History of mathematical notations, which has a thorough discussion of the history of the notation and nomenclature of powers.