Question

What is the cube root of -729a^9b^6

a.-9a^3b^2
b.-9a^2b^3
c.-8a^3b^2
d.-8a^2b^3

Answer 1

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