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Question
Simplify the following and express with positive index:
3p-2q3 ÷ 2p3q-2
Solution
3p-2q3 ÷ 2p3q-2
= `(3"p"^-2"q"^3)/(2"p"^3"q"^-2)`
= `(3)/(2)["p"^-2/"p"^3 xx "q"^3/"q"^-2]`
= `(3)/(2)[("p"^-2 ÷ "p"^3) xx ("q"^3 ÷ "q"^-2)]`
= `(3)/(2)[("p"^(-2-3)) xx ("q"^(3 - (-2)))]` .....(Using am ÷ an = am-n)
= `(3)/(2)[("p"^-5) xx ("q"^5)]`
= `(3)/(2)[(1/"p"^5) xx ("q"^5)]`
= `(3"q"^5)/(2"p"^5)`.
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