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(-4y^3)^2

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

Simplifying (-4y^3)^2

This expression involves a few key concepts in algebra: exponents, multiplication, and the order of operations. Let's break it down step-by-step.

Understanding the Components

  • (-4y^3): This is a monomial, meaning it's a single term with a coefficient (-4) and a variable (y) raised to a power (3).
  • ^2: This is an exponent, indicating that the entire monomial (-4y^3) should be multiplied by itself.

Applying the Rules

  1. Distributing the Exponent: When raising a product to a power, we distribute the exponent to each factor within the parentheses.

    • (-4y^3)^2 = (-4)^2 * (y^3)^2

  2. Simplifying the Exponents: When raising a power to another power, we multiply the exponents.

    • (-4)^2 * (y^3)^2 = 16 * y^(3*2) = 16y^6

The Final Answer

Therefore, (-4y^3)^2 simplifies to 16y^6.

Key Points to Remember

  • Order of operations (PEMDAS/BODMAS): Parentheses/Brackets first, then Exponents, Multiplication and Division (from left to right), finally Addition and Subtraction (from left to right).
  • Exponent rules: When raising a product to a power, distribute the exponent to each factor. When raising a power to another power, multiply the exponents.

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