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The expression provided is:

\[
\left( -3x^3 y^4 \right)^4
\]

To fully simplify it, we will apply the power to each term inside the parentheses using the power of a product rule:

\[
(a \cdot b)^n = a^n \cdot b^n
\]

### Step-by-step simplification:
1. Apply the exponent of 4 to each part of the expression:
   \[
   (-3)^4 \cdot (x^3)^4 \cdot (y^4)^4
   \]

2. Simplify each term:
   - \((-3)^4 = 81\)
   - \((x^3)^4 = x^{3 \cdot 4} = x^{12}\)
   - \((y^4)^4 = y^{4 \cdot 4} = y^{16}\)

### Final simplified expression:
\[
81x^{12}y^{16}
\]

This is the fully simplified form of the expression.

Would you like any further details, or do you have any other questions?

Here are 5 related questions for practice:
1. How would you simplify \((2x^2y^3)^5\)?
2. What happens when a negative number inside a parenthesis is raised to an even exponent?
3. Can you simplify \((-4x^5y^2)^3\)?
4. What is the difference between the rules for exponents in multiplication and addition?
5. How do you simplify expressions like \((a^m b^n)^p\)?

**Tip:** When raising a product of terms to a power, remember to apply the exponent to each term individually!

Learn how to fully simplify the expression (-3x^3y^4)^4 using the power of a product and power of a power rules. The detailed step-by-step solution covers key algebraic concepts in exponentiation. Suitable for students in Grades 8-10.

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