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(4m^2n)^2/2m^5n

2 min read Jun 16, 2024
(4m^2n)^2/2m^5n

Simplifying Algebraic Expressions: (4m^2n)^2 / 2m^5n

This article will guide you through simplifying the algebraic expression (4m^2n)^2 / 2m^5n. Let's break down the process step-by-step.

Understanding the Expression

The expression involves:

  • Exponents: We have (4m^2n)^2, which means we need to square the entire term within the parentheses.
  • Division: The expression involves dividing the squared term by 2m^5n.

Simplifying the Expression

  1. Square the term in parentheses:

    (4m^2n)^2 = 4^2 * (m^2)^2 * n^2 = 16m^4n^2

  2. Rewrite the expression:

    Now we have: 16m^4n^2 / 2m^5n

  3. Simplify by dividing coefficients and subtracting exponents:

    • Coefficients: 16 / 2 = 8
    • m exponents: m^4 / m^5 = m^(4-5) = m^-1
    • n exponents: n^2 / n = n^(2-1) = n^1

  4. Combining terms:

    This gives us: 8 * m^-1 * n^1 = 8n/m

Final Answer

Therefore, the simplified form of (4m^2n)^2 / 2m^5n is 8n/m.

Key Points to Remember

  • Exponent rules: When raising a term to a power, we apply the power to each factor within the term.
  • Division of exponents: When dividing terms with the same base, we subtract the exponents.
  • Negative exponents: A negative exponent indicates a reciprocal. For example, m^-1 = 1/m.

By applying these rules, we successfully simplified the given algebraic expression.

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