Question

If $a>b,$ where $a,b<0,$ then $a^r<b^r$ when

• A. $r=4$
• B. $r=-3$
• C. $r=-2$
• D. $r=7$

Answer 1

Answer: (A), (B)

The correct options are
A $r=4$
B $r=-3$

Here, $a>b$
when $r=$ even positive integer $a^r,b^r>0$
$\Rightarrow a^r<b^r$
$\therefore a^4<b^4$

when $r=$ odd positive integer $a^r,b^r<0$
$\Rightarrow a^r>b^r$
$\therefore a^7>b^7$

when $r=$ even negative integer $a^r,b^r>0$
$\Rightarrow a^r>b^r$
$\therefore a^{-2}>b^{-2}$

when $r=$ odd negative integer $a^r,b^r<0$
$\Rightarrow a^r<b^r$
$\therefore a^{-3}<b^{-3}$