Question

Which of the following statement regarding the sign of $(-5{)}^{2021}$ is correct?

• A. $(-5{)}^{2021}$ is a positive number.
• B. $(-5{)}^{2021}$ is a negative number.

Answer 1

The correct option is B $(-5{)}^{2021}$ is a negative number.

As we know,

$\bullet$ Negative base raised to an even power always gives a positive value.
$\bullet$ Negative base raised to an odd power always gives a negative value.

Hence, for $a<0,$

• $a^n$ is positive if $n$ is even, and
• $a^n$ is negative if $n$ is odd

Now, in $(-5{)}^{2021},$

• base $=(-5),$ which is negative
• exponent/power $=2021,$ which is odd.

Therefore, as per the above discussion, $(-5{)}^{2021}$ is a negative number.

$\therefore$ Option (b.) is the correct one.