Question

For $a<0,$ select the correct statement(s).

• A. $a^n=$ positive, if $n$ is even
• B. $a^n=$ positive, if $n$ is odd
• C. $a^n=$ negative, if $n$ is even
• D. $a^n=$ negative, if $n$ is odd

Answer 1

Answer: (A), (D)

$a^n=$ negative, if $n$ is odd

• A negative base raised to an even power always gives a positive value.

For example: In $(-2{)}^2,$ negative base $=-2$ and even power $=2$.

$\therefore (-2{)}^2=(-2)\times (-2)=4\text{(positive value)}$

• A negative base raised to an odd power always gives a negative value.

For example: In $(-2{)}^3,$ negative base $=-2$ and odd power $=3.$

$\therefore (-2{)}^3=(-2)\times (-2)\times (-2)=-8\text{(negative value)}$