What is b^0 for a nonzero b?

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Multiple Choice

What is b^0 for a nonzero b?

Explanation:
Raising a nonzero number to the zero power yields 1. This follows the exponent rule a^m / a^n = a^{m-n} for a ≠ 0. If you divide the same power by itself, you get 1, and that equals a^{m-m} = a^0. So b^0 = 1 for any nonzero b. The base being nonzero matters because it lets us divide by the same base without hitting division by zero. The other possibilities don’t fit the exponent rule: it isn’t 0 or b, since those would correspond to different exponents, and it isn’t undefined because the base is nonzero.

Raising a nonzero number to the zero power yields 1. This follows the exponent rule a^m / a^n = a^{m-n} for a ≠ 0. If you divide the same power by itself, you get 1, and that equals a^{m-m} = a^0. So b^0 = 1 for any nonzero b. The base being nonzero matters because it lets us divide by the same base without hitting division by zero. The other possibilities don’t fit the exponent rule: it isn’t 0 or b, since those would correspond to different exponents, and it isn’t undefined because the base is nonzero.

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