化简 $\left(\dfrac{-2p^{3}}{q^{-1}}\right)^{2}\div\left(\dfrac{8q^{4}}{p^{3}}\right)^{\tfrac{1}{3}}$ ，并将你的答案表示为正指数形式。

它不会直接告诉你答案，而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的

完整解法

1. Simplify the first bracket and square it.

$\left(\dfrac{-2p^3}{q^{-1}}\right)^2=\left(-2p^3\times q\right)^2=(-2p^3q)^2=4p^6q^2$

2. Simplify the second bracket using the fractional index.

$\left(\dfrac{8q^4}{p^3}\right)^{\frac13}=\dfrac{8^{\frac13}q^{\frac43}}{p}=\dfrac{2q^{\frac43}}{p}$

3. Divide the two simplified expressions and write the final answer with positive indices.

$4p^6q^2\div \dfrac{2q^{\frac43}}{p}=4p^6q^2\times \dfrac{p}{2q^{\frac43}}$
$=2p^7q^{2-\frac43}=2p^7q^{\frac23}$

答案

$\dfrac{4p^7}{q^3}$

AI 分析，可能出错

用 AI 批改，圈出写错的那一步，并自动将你的薄弱点存入错题本，形成你的错因库。