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What's the general form for $x^y$? What's the specialized form for $x^1$ and $x^0$?

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    $x^0$ is "unity" or "one". :)2010-12-30
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    On a less frivolous note, the $x$ term (variable raised to the first power) in a polynomial is usually called the *linear* term. One can also speak of *quintic* ($x^5$), *sextic* ($x^6$), *septic* ($x^7$)... terms.2010-12-30
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    In that context, $x^0$ (times some coefficient) would be called the *constant* term.2010-12-30
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    Also, $x^2$ is often referred to as the "quadratic" term rather than the so-called "square" term, especially in the context of polynomials.2010-12-30

2 Answers 2

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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.

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$x$ 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.