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!