Question

Check if the following relations are correct if $n$ represents an odd integer.

• A. $-(-8{)}^n<0$
• B. $-(-22{)}^{n-1}>0$
• C. $(-5\times 3{)}^{n+1}<0$
• D. $-(-4\times 5{)}^n>0$

Answer 1

The correct option is D $-(-4\times 5{)}^n>0$

$\bullet$ In the $(-8{)}^n$, base $(-8)$ is negative and exponent, $n$, is odd. Hence, in the result of $(-8{)}^n$,a negative sign will come, and $-(-8{)}^n>0$ always. So, the relation $-(-8{)}^n<0$ is INCORRECT.

$\bullet$ In $(-22{)}^{n-1}$, base, $(-22)$, is negative and exponent, $n-1$, is even as $n$ is odd. Hence, in the result of $(-22{)}^{n-1}$,a positive sign will come, and $-(-22{)}^{n-1}<0$ always. So, the relation $-(-22{)}^{n-1}>0$ is INCORRECT.

$\bullet$ In $(-5\times 3{)}^{n+1}=(-15{)}^{n+1}$, base, $(-15)$, is negative and exponent, $n+1$, is even as $n$ is odd. Hence, in the result of $(-15{)}^{n+1}$,a positive sign will come, and $(-5\times 3{)}^{n+1}>0$ always. So, the relation $(-5\times 3{)}^{n+1}<0$ is incorrect.

$\bullet$ In $(-4\times 5{)}^n=(-20{)}^n$, base, $(-20)$, is negative and exponent, $n$, is odd. Hence, in the result of $(-20{)}^n$,a negative sign will come, and $-(-4\times 5{)}^n>0$ always. So, the relation $-(-4\times 5{)}^n>0$ is correct.