Simplifying (5x^3y^4)^4
In mathematics, simplifying expressions often involves using the rules of exponents. Let's break down how to simplify the expression (5x^3y^4)^4.
Understanding the Rules
The key rule we need here is the power of a product rule:
(ab)^n = a^n * b^n
This means that when raising a product to a power, we can distribute the power to each factor within the product.
Applying the Rule

Distribute the exponent: We start by distributing the exponent of 4 to each factor within the parentheses: (5x^3y^4)^4 = 5^4 * (x^3)^4 * (y^4)^4

Simplify exponents: We now apply another rule of exponents: (a^m)^n = a^(m*n). 5^4 * (x^3)^4 * (y^4)^4 = 625 * x^12 * y^16
Final Result
The simplified form of (5x^3y^4)^4 is 625x^12y^16.