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(7n^3)^2

2 min read Jun 16, 2024
(7n^3)^2

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

  1. Apply the exponent to both the coefficient and the variable:

    • (7n^3)^2 = 7^2 * (n^3)^2

  2. Simplify the coefficient:

    • 7^2 = 49

  3. 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

  4. Combine the simplified terms:

    • 49 * n^6 = 49n^6

Final Answer

Therefore, the simplified form of (7n^3)^2 is 49n^6.

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