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(2x^3y)^4

2 min read Jun 16, 2024
(2x^3y)^4

Simplifying (2x³y)⁴

In mathematics, simplifying expressions is a crucial skill. Let's break down how to simplify the expression (2x³y)⁴.

Understanding the Basics

  • Exponents: An exponent indicates how many times a base is multiplied by itself. In this case, the base is (2x³y) and the exponent is 4.
  • Order of Operations: We follow the order of operations (PEMDAS/BODMAS) to simplify 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. Distribute the exponent: We apply the exponent to each term inside the parentheses.
    (2x³y)⁴ = 2⁴ * (x³)⁴ * y⁴

  2. Simplify the exponents: 2⁴ * (x³)⁴ * y⁴ = 16 * x¹² * y⁴

  3. Final Simplified Expression: 16 * x¹² * y⁴ = 16x¹²y⁴

Conclusion

Therefore, the simplified form of (2x³y)⁴ is 16x¹²y⁴. This process demonstrates how to use exponent rules and the order of operations to effectively simplify mathematical expressions.

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