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(-4c^3d)^2

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

Simplifying (-4c^3d)^2

In this article, we will explore how to simplify the expression (-4c^3d)^2.

Understanding the Basics

  • Exponents: The exponent (the small number written above and to the right of a base) indicates how many times the base is multiplied by itself. For example, x² means x multiplied by itself twice (x * x).
  • Parentheses: When an expression is enclosed in parentheses and raised to a power, the entire expression within the parentheses is multiplied by itself the number of times indicated by the exponent.

Applying the Rules

  1. Distribute the exponent: When an expression inside parentheses is raised to a power, each term within the parentheses is raised to that power. In this case, we have:

    (-4c^3d)^2 = (-4)^2 * (c^3)^2 * (d)^2

  2. Simplify each term:

    • (-4)^2 = 16
    • (c^3)^2 = c^(3*2) = c^6 (Remember: When raising a power to another power, multiply the exponents)
    • (d)^2 = d^2

  3. Combine the terms: 16 * c^6 * d^2 = 16c^6d^2

Final Result

Therefore, the simplified expression for (-4c^3d)^2 is 16c^6d^2.

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