## Simplifying (3n^4)^2

In mathematics, simplifying expressions is a fundamental skill. Let's break down how to simplify the expression (3n^4)^2.

### Understanding the Rules

The key here is understanding the **order of operations** and the **rules of exponents**.

**Order of operations**(often remembered by the acronym PEMDAS or BODMAS) tells us to perform operations within parentheses first.**Rules of exponents**state that when raising a power to another power, we multiply the exponents.

### Simplifying the Expression

**Focus on the parentheses:**We have (3n^4) raised to the power of 2.**Apply the rule of exponents:**We multiply the exponents inside the parentheses by the exponent outside. This gives us: 3^(1*2) * n^(4*2)**Calculate:**This simplifies to 3^2 * n^8**Final result:**The simplified expression is**9n^8**.

### Explanation

In essence, (3n^4)^2 means we're multiplying (3n^4) by itself twice:

(3n^4)^2 = (3n^4) * (3n^4)

By applying the rules of exponents, we efficiently arrive at the simplified form 9n^8.

### Conclusion

Simplifying expressions like (3n^4)^2 is a crucial step in understanding and manipulating mathematical equations. By applying the order of operations and rules of exponents, we can effectively reduce complex expressions to their simplest forms.