To determine which expression is equivalent to [tex]\(5 \sqrt[3]{6c} + 7 \sqrt[3]{6c}\)[/tex], we need to follow these steps:
1. Identify like terms: Both terms have [tex]\(\sqrt[3]{6c}\)[/tex] as a common factor.
2. Combine the coefficients: The coefficients are 5 and 7.
To combine these like terms, sum the coefficients and then multiply by the common factor [tex]\(\sqrt[3]{6c}\)[/tex].
Let's break it down:
[tex]\[
5 \sqrt[3]{6c} + 7 \sqrt[3]{6c}
\][/tex]
We sum the coefficients [tex]\(5 + 7\)[/tex]:
[tex]\[
5 + 7 = 12
\][/tex]
Now, multiply this sum by the common factor [tex]\(\sqrt[3]{6c}\)[/tex]:
[tex]\[
12 \sqrt[3]{6c}
\][/tex]
Hence, the expression [tex]\(5 \sqrt[3]{6c} + 7 \sqrt[3]{6c}\)[/tex] is equivalent to [tex]\(12 \sqrt[3]{6c}\)[/tex].
So, the correct answer is:
C. [tex]\(12 \sqrt[3]{6c}\)[/tex]
