Q.Simplify $\dfrac{a^3\,b^{-2}}{a^{-1}\,b^4}$, expressing the final answer using positive indices only.

Simplify the $a$ terms and the $b$ terms separately using the quotient law, then convert any negative indices to positive form.

Simplify the $a$ terms (quotient law):

Simplify the $b$ terms (quotient law):

Combine:

Convert to positive indices only:

$a^4\,b^{-6} = \frac{a^4}{b^6}$ …

Mishandling the double-negative when dividing by $a^{-1}$ (wrongly computing $3-(-1)$ as $2$ instead of $4$), and separately forgetting the sign …