Yes, absolutely. And 0 is an even number.
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Negative numbers to even powers will be positive, negative numbers to odd powers will be negative. The answer is -16,384.
To start with, when you multiply an even number of negative numbers, the answer is positive. When you multiply an odd number of negative numbers, the answer is negative. When you multiply any number of positive numbers, the answer is always positive. For positive numbers, the value of a power is always positive. For negative numbers, the value of an odd power is negative, and the value of an even power is positive. Finding roots is the inverse of taking powers, so that an odd-root function can be evaluated for any value of x. An even-root function, however, cannot be evaluated when the value of x is negative, since an even power can never result in a negative answer. The domain of an odd root function is all real numbers; the domain of an even root function is the non-negative real numbers.
The square of every positive or negative even whole number is a positive even whole number. The square of every positive or negative odd whole number is a positive odd whole number. There are an infinite number of each kind.
Let's assume for a moment we're not thinking about negative numbers. Only counting numbers from 0-49, there is the same number even as odd so the answer is no. If you didn't include 0, then the answer would be yes. If you do include negative numbers, then there are an infinite number of both odd and even numbers. In this case it doesn't seem to make sense to say there are more odd numbers than even numbers so the answer is no. In short: No. Yes if it's only 1-49.
There is no such pattern because there are no even odd numbers. Odd numbers, by definition, are odd and therefore, not even.