Subjects algebra

Exponent Zero 808212

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1. The problem states: "Any number raised to 0 is equal to 1." We want to understand why this is true. 2. The rule for exponents is: $$a^m \times a^n = a^{m+n}$$ where $a$ is any nonzero number, and $m,n$ are integers. 3. Using this rule, consider $a^m \times a^0 = a^{m+0} = a^m$. 4. To satisfy this equality, $a^0$ must be 1 because multiplying by 1 does not change the value: $$a^m \times a^0 = a^m \implies a^0 = 1$$. 5. This holds for any nonzero number $a$. Therefore, any number raised to the power 0 equals 1. Final answer: $$a^0 = 1$$ for any $a \neq 0$.