[tex]\displaystyle\bf\\\sqrt[3]{-729a^9b^6}=\\\\=\sqrt[3]{\Big(-1\Big)^3\times\Big(9\Big)^3\times\Big(a\Big)^{3\times3}\times\Big(b\Big)^{2\times3}}=\\\\\\=\sqrt[3]{\Big(-1\Big)^3\times\Big(9\Big)^3\times\Big(a^3\Big)^3\times\Big(b^2\Big)^{3}}=\\\\\\=(-1)\times9\times a^3\times b^2=\\\\=\boxed{\bf-9a^3b^2}\\\\Correct~answer\!:~~~a)[/tex]
