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**Question 1: True or False?**

To determine whether the work shown for simplifying the expression \((34)^{-3}\) is correct, we need to analyze the steps.

1. The expression \((34)^{-3}\) simplifies to \(\frac{1}{(34)^3}\).
2. The expression simplifies further to \(\frac{1}{34^3}\).

The work that's shown in the question seems incorrect. It appears that it involves manipulating the terms inappropriately, resulting in a nonsensical conclusion. Without seeing the complete steps, it is difficult to analyze fully, but the answer generally is:

**False.**

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**Question 2: Simplify the expression \((3p^3n^2)^4\):**

To simplify this expression, we use the power of a product property and the power of a power property of exponents.

1. Apply the exponent to each part of the product:
\[
(3^4)(p^{3 \cdot 4})(n^{2 \cdot 4})
\]

2. Calculate each part:
\[
3^4 = 81
\]
\[
p^{3 \cdot 4} = p^{12}
\]
\[
n^{2 \cdot 4} = n^8
\]

3. Combine the results:
\[
81p^{12}n^8
\]

Thus, the simplified expression is:
\[
\boxed{81p^{12}n^8}
\]