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(5x^4y^3)^3

less than a minute read Jun 16, 2024
(5x^4y^3)^3

Simplifying (5x⁴y³)^3

In mathematics, simplifying expressions often involves applying various rules and properties. One such expression is (5x⁴y³)^3, which we can simplify using the properties of exponents.

Understanding the Properties

Here's a breakdown of the properties we'll use:

  • Power of a Product: (ab)^n = a^n * b^n
  • Power of a Power: (a^m)^n = a^(m*n)

Applying the Properties

  1. Apply the Power of a Product: (5x⁴y³)^3 = 5^3 * (x⁴)^3 * (y³)^3

  2. Apply the Power of a Power: 5^3 * (x⁴)^3 * (y³)^3 = 5³ * x^(43) * y^(33)

  3. Simplify: 5³ * x^(43) * y^(33) = 125x¹²y⁹

The Final Result

Therefore, the simplified form of (5x⁴y³)^3 is 125x¹²y⁹.

This simplification demonstrates how understanding and applying exponent properties can help us manipulate and simplify complex expressions effectively.

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