Anything multiplied by 0 is 0 right so why does x number raised to the power of 0 = 1? isnt it x^0 = x*0 (im turning grade 10 and i asked my teacher about this he told me its because its just what he was taught 💀)
In: Mathematics
I was on the hiring committee for the math department of a community college and we would role play students in a lesson about exponential functions given by the applicant. We would ask your question. An answer no better than what your teacher gave was close to eliminating any hiring chance by itself. Reasonable answers include some aspects of the following:
It is a definition and could be defined however one wants. Defining it as 1 is the most useful definition mathematically for both consistency and usability. For example,
since anything other than zero divided by itself is 1 we have x^n / x^n is 1. But we also have a rule that it should equal x^(n-n) = x^0. For that rule to still work we need x^0 =1. It also maintains the pattern of making the exponent one smaller mean that the result is divided by x. e.g. going from x^3 to x^2 one divides by x. Going from x^2 to x one divides by x. Going from x^1 to x^0 one divides by x and x/x = 1. A similar idea leads to why x^(-n) = 1/x^n which is allows scientific notation to handle very small as well as very large numbers. One more thing to consider is an analogy with addition. Adding 0 to a number does not change a number (does nothing). Exponentiation is about multiplication and for multiplication multiplying by 1 does not change a number (does nothing) so you can think of a zero exponent as doing nothing in terms of multiplication.
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