Question

What will be the sign of the product if we multiply together:

(a) (-3),2m+1 times where m is a natural number?

(b) (-4),2m times where m is a natural number?

Answer 1

(1) 2m+1 always represent an odd number
also,
when a negative integer have an odd number as power than the result is also negative
so,
(-3)^2m+1 is negative for all m belongs to natural numbers
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(2) 2m always represent an even number
also,
when a negative integer have an even number as power than the result is positive
so,
(-4)^2m is positive for all m belongs to natural numbers