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Why do equations equal 1 when exponent is 0?

for example (3xyz)0(is the exponent)…why does this equal 1???Why do equations with an exponent of 0 always equal 1?? if I get the right answer and a source I get extra credit in math class…so if anyone knows please explain and list the sourse or link of source…thank you.

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Answer #1

Any number (except 0) with exponent 0 is defined as 1. It won’t ALWAYS equal 1, but it’s always defined as 1.

In algebra theres a rule called the rule of exponents for quotients that states: a^m/a^m = a^m-m = a^0. But a cannot = 0. So: a^m/a^m = 1.

(Also when considering rational expressions (fractions) if the numerator and the denominator are the same it’s equal to 1.)

0^0 can equal any number so it’s the only exception to the rule.

Edit: I didn’t use a source, unless my math prof counts? lol we learnt this in class like 2 years ago…

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