Select the equivalent expression.

To simplify the expression \(\left(x^{-3}\cdot y^{3}\right)^{-7}\), we will apply the properties of exponents.

1. Start by applying the power of a product rule, which states that \((ab)^n = a^n \cdot b^n\).

\[
\left(x^{-3} \cdot y^{3}\right)^{-7} = \left(x^{-3}\right)^{-7} \cdot \left(y^{3}\right)^{-7}
\]

2. Now, we can simplify each component. Using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\):

\[
\left(x^{-3}\right)^{-7} = x^{-3 \cdot (-7)} = x^{21}
\]

\[
\left(y^{3}\right)^{-7} = y^{3 \cdot (-7)} = y^{-21}
\]

3. Combining these results, we have:

\[
\left(x^{-3} \cdot y^{3}\right)^{-7} = x^{21} \cdot y^{-21}
\]

So the equivalent expression is:

\[
x^{21} \cdot y^{-21}
\]

Thus, the answer is:

Choice C: \[x^{21}\cdot y^{-21}\]