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

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

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

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.