The given expression is [tex] 3b^2*(\sqrt[3]{54a}) + 3*(\sqrt[3]{2ab^6}) [/tex]
This can be simplified as :
= [tex] 3*b^2*(\sqrt[3]{27 *2*a}) + 3*(\sqrt[3]{2*a*b^6}) [/tex]
We know that: [tex] \sqrt[3]{27} = 3 [/tex]
Similarly we also can simplify: [tex] \sqrt[3]{b^6} = b^2 [/tex]
So our expression will look like this:
= [tex] 3*3*b^2*(\sqrt[3]{2a}) + 3*b^2*(\sqrt[3]{2a}) [/tex]
= [tex] 9b^2*(\sqrt[3]{2a}) + 3b^2*(\sqrt[3]{2a}) [/tex]
=[tex] \sqrt[3]{2a}*(9b^2 + 3b^2) [/tex]
=[tex] \sqrt[3]{2a}*(12b^2) [/tex]
This can also be written as:
[tex] 12b^2(\sqrt[3]{2a}) [/tex]
So the Answer is Option B
