[tex]3ab^2\times\sqrt[3]{b}\text{ (option A)}[/tex]Explanation:[tex]\sqrt[3]{27a^{^{}3}b^7}[/tex]
let's factorise in powers of 3 or in cube:
27 = 3³
b^7 = b^6 × b
b^6 = (b²)³
b^7 = (b²)³ × b
Then insert the above into the expression:
[tex]\begin{gathered} \sqrt[3]{27a^{^{}3}b^7}\text{ =}\sqrt[3]{3^3\times a^3\times(b^2)^3\times b} \\ =\text{ }\sqrt[3]{(3\times a\times b^2)^3}\times\sqrt[3]{b}=3ab^2\times\sqrt[3]{b} \\ =3ab^2\times\sqrt[3]{b}\text{ (option A)} \end{gathered}[/tex]
