Question #4b94f

1 Answer
Nov 6, 2016

Answer:

Perhaps someone else can add a more in depth explanation

Explanation:

This is a subject that is argued about a lot.

#color(blue)("View point 1:")#

Any number raised to the power of zero is 1.
Hence: #0^0=1#

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#color(blue)("View point 2: ")#

Some argue that 0 is not a number it is a placeholder so

#0^0!=1# as #0^0# is 'undefined'
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The problem stems from the following:

Consider the example #3^2/3^2 = 3^(2-2)=3^0=1# which is true.

However to end up with #0^0# we would need to have

#0^x/0^x = 0^(x-x)=0^0#

However #0^x=0# so we have #0/0# and to have 0 as the denominator makes the whole thing 'undefined'.

This in turn makes #0^0# undefined.

#color(purple)("Bit of a dilemma, isn't it!")#