Question

On multiplying ___ by $3^{-5},$ we get $9^2$.

• A. $3^7$
• B. $3^8$
• C. $3^9$
• D. $3^{10}$

Answer 1

The correct option is C $3^9$

Let $x$ be multiplied by $3^{-5}$ to get $9^2.$
i.e., $x\times 3^{-5}=9^2$
But, $9^2=(3^2{)}^2=3^4.(\because (a^m{)}^n=a^{mn})$

$\therefore x\times 3^{-5}=3^4$
$⟹x=\frac{3^4}{3^{-5}}$
$⟹x=3^{4-(-5)}=3^9(\because \frac{a^m}{a^n}=a^{m-n})$
Therefore, we get $9^2$ on multiplying $3^9$ by $3^{-5}.$