Answer :

To determine the simplified form of the expression [tex]\((\sqrt[3]{a})^6\)[/tex], let's proceed step by step.

1. Interpret the expression:
[tex]\[ (\sqrt[3]{a})^6 \][/tex]
The term [tex]\(\sqrt[3]{a}\)[/tex] can be written using exponential notation as [tex]\(a^{1/3}\)[/tex].

2. Re-write the expression using exponents:
[tex]\[ (a^{1/3})^6 \][/tex]

3. Apply the power of a power property for exponents:
When you raise a power to another power, you multiply the exponents. Thus:
[tex]\[ (a^{1/3})^6 = a^{(1/3) \cdot 6} \][/tex]

4. Calculate the new exponent:
[tex]\[ (1/3) \cdot 6 = 2 \][/tex]

5. Simplify the expression:
[tex]\[ a^{2} \][/tex]

Therefore, the simplified form of the expression [tex]\((\sqrt[3]{a})^6\)[/tex] is [tex]\(a^2\)[/tex].

So, the correct answer is:
[tex]\[ \boxed{B. \quad a^2} \][/tex]