Simplifying (7n^3)^2
In mathematics, simplifying expressions is a fundamental skill. Let's break down how to simplify the expression (7n^3)^2.
Understanding Exponents and Order of Operations
 Exponents: An exponent indicates how many times a base number is multiplied by itself. In this case, the base is 7n^3 and the exponent is 2.
 Order of Operations: We follow the order of operations (PEMDAS/BODMAS) to solve mathematical expressions:
 Parentheses (or Brackets)
 Exponents (or Orders)
 Multiplication and Division (from left to right)
 Addition and Subtraction (from left to right)
Simplifying the Expression

Apply the exponent to both the coefficient and the variable:
 (7n^3)^2 = 7^2 * (n^3)^2

Simplify the coefficient:
 7^2 = 49

Apply the power of a power rule: When raising a power to another power, multiply the exponents.
 (n^3)^2 = n^(3*2) = n^6

Combine the simplified terms:
 49 * n^6 = 49n^6
Final Answer
Therefore, the simplified form of (7n^3)^2 is 49n^6.