What is the zero exponent rule such as $x^3/x^3$ ?

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Answer 1 · 2016-07-09T15:35:56

$x^3/x^3 = x^0 = 1$

Any number to the power of 0 is equal to 1.

$x^3/x^3$ can be calculated in two ways:

Method 1. Cancel because $"anything"/"itself" = 1$

$6/6 = 1, " " (-8)/(-8) = 1$ etc

$cancel(x^3)^1/cancel(x^3)^1 = 1$

Method 2: Using laws of indices,:
$x^3/x^3 = x^(3-3) = x^0$

However there can only be one answer, which means that the two answers from the different methods have to mean the same thing.

:. $x^3/x^3 = x^0 = 1$

What is the zero exponent rule such as x^3/x^3x^3/x^3?