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
“Raised to a power” kind of means “how many times is the base number multiplied by itself?” So, you get something like 3² = 3×3 = 9, or 3³ = 3x3x3 = 27, right? The power expresses “how many copies of the number are multipled together.”
When you multiply 0 copies of the base number, you’re not left with the additive identity, 0, but the multiplicative identity, 1.
3³ = 1x3x3x3, and 3² = 1x3x3, and 3¹ = 1×3 and 3⁰ = 1 with no copies of 3 to multiply by.
So, for your question, you aren’t multiplying by zero, which multiplicatively turns the equation to zero, you’re adding zero copies of the base number into a multiplicative expression, where the multiplicative identity, 1, can always exist without changing the result. Since 1 is the only thing in the expression (as you didn’t add any copies of the base number to the expression), the result is just 1.
Latest Answers