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]
