Simplify $\left(\sqrt[3]{\dfrac{a^{15}}{b^{6}}}\right)^{-2}$ , leaving your answer in positive indices.

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

1. Rewrite the cube root using fractional indices and simplify inside powers.

$\left(\sqrt[3]{\dfrac{a^{15}}{b^6}}\right)^{-2}=\left(\left(\dfrac{a^{15}}{b^6}\right)^{\frac13}\right)^{-2}$
$=\left(\dfrac{a^5}{b^2}\right)^{-2}$

2. Apply the negative index and leave the answer with positive indices.

$\left(\dfrac{a^5}{b^2}\right)^{-2}=\left(\dfrac{b^2}{a^5}\right)^2$
$=\dfrac{b^4}{a^{10}}$

Answer

$\dfrac{b^4}{a^{10}}$

AI analysis — may contain mistakes.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.