Question
Simplify the following and express with positive index:$3p^{-2}q^3 \div 2p^3q^{-2}$
✓
Answer
$3 p^{-2} q^3 \div 2 p^3 q^{-2}$
$=\frac{3 p^{-2} q^3}{2 p^3 q^{-2}}$
$=\frac{3}{2}\left[\frac{p^{-2}}{p^3} \times \frac{q^3}{q^{-2}}\right]$
$=\frac{3}{2}\left[\left(p^{-2} \div p^3\right) \times\left(q^3 \div q^{-2}\right)\right]$
$=\frac{3}{2}\left[\left(p^{-2-3}\right) \times\left(q^{3-(-2)}\right)\right] \ldots($Using $a^m \div a^n=a^{m-n})$
$=\frac{3}{2}\left[\left(p^{-5}\right) \times\left(q^5\right)\right]$
$=\frac{3}{2}\left[\left(\frac{1}{p^5}\right) \times\left(q^5\right)\right]$
$=\frac{3 q^5}{2 p^5} .$
$=\frac{3 p^{-2} q^3}{2 p^3 q^{-2}}$
$=\frac{3}{2}\left[\frac{p^{-2}}{p^3} \times \frac{q^3}{q^{-2}}\right]$
$=\frac{3}{2}\left[\left(p^{-2} \div p^3\right) \times\left(q^3 \div q^{-2}\right)\right]$
$=\frac{3}{2}\left[\left(p^{-2-3}\right) \times\left(q^{3-(-2)}\right)\right] \ldots($Using $a^m \div a^n=a^{m-n})$
$=\frac{3}{2}\left[\left(p^{-5}\right) \times\left(q^5\right)\right]$
$=\frac{3}{2}\left[\left(\frac{1}{p^5}\right) \times\left(q^5\right)\right]$
$=\frac{3 q^5}{2 p^5} .$
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