If n is even, the sign of the product of n negative even numbers can be determined using the equation [tex](-1)^n[/tex]
If n is odd, the sign of the product of n negative odd numbers can be determined using the equation [tex](-1)^{n+1}[/tex]
Product of two negative numbers is Positive
Product of three negative numbers is negative
Let the exponent showing frequency of negative numbers be n
For two negative numbers, n = 2
product of two negative numbers will be [tex](-1)^2 = 1(+ve)[/tex]
Product of three negative numbers will be [tex](-1)^3 = -1(+ve)[/tex]
Since 2 is an even number and 3 is an odd number, we can conclude that:
If n is even, the sign of the product of n negative even numbers can be determined using the equation [tex](-1)^n[/tex]
If n is odd, the sign of the product of n negative odd numbers can be determined using the equation [tex](-1)^{n+1}[/tex]
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