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#