%5E2.jpeg "(3n^4)^2")
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^(12) * n^(42)
- 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.