Yes. Any multiplication involving an odd number of negative operands will be negative (assuming non-zero operands).
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The multiplication rule of thumb always states that a negative number times a negative number results in a positive number. Since an even number is always divisible by two, any value raised to an even integer power will result in a positive number. However, a basic proof is presented as follows: (-A) * (-A) = A^2 ((-A) * (-A)) ^ 2 = ((-A * -A) * (-A * -A)) = A^2 * A^2 = A ^ 4 ...
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Yes, a negative number raised to an odd power will simplify to a negative number. This is because when you multiply two negative numbers together, the result is always a positive number. However, when you raise a negative number to an odd power, the negative sign remains, resulting in a negative number. This is a fundamental property of exponents and is consistent across all mathematical operations involving negative numbers.
Any number raised to the power of zero is just 1.