Question

Difficulty: EasyEven-Odd Properties and Sign Rules

If $m$ is an even integer and $n$ is an odd integer, what is the value of $(-1)^m + (-1)^n$ ?

Answer: 0

Since

m

is an even integer,

(-1)^m = 1

. Since

n

is an odd integer,

(-1)^n = -1

. Adding

1

and

-1

yields

0

Evaluate

(-1)^m

for an even integer

m

(-1)^m = 1

Raising

-1

to an even integer power always results in

1

Evaluate

(-1)^n

for an odd integer

n

(-1)^n = -1

Raising

-1

to an odd integer power always results in

-1

Sum the two evaluated expressions

1 + (-1) = 0

Combining

1

and

-1

equals

0

Exponent sign rules for even and odd powers

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