To simplify the expression [tex]\( 5 \sqrt[3]{6c} + 7 \sqrt[3]{6c} \)[/tex], we need to combine the like terms.
Both terms contain the same cube root, [tex]\( \sqrt[3]{6c} \)[/tex]. Therefore, we can factor out [tex]\( \sqrt[3]{6c} \)[/tex] from each term:
[tex]\[
5 \sqrt[3]{6c} + 7 \sqrt[3]{6c} = (5 + 7) \cdot \sqrt[3]{6c}
\][/tex]
Next, we add the coefficients:
[tex]\[
5 + 7 = 12
\][/tex]
Thus, the simplified expression becomes:
[tex]\[
12 \sqrt[3]{6c}
\][/tex]
So, the correct answer is:
C. [tex]\( 12 \sqrt[3]{6c} \)[/tex]
