%5E5.jpeg "(3x^2y)^5")
Simplifying (3x²y)⁵
In mathematics, simplifying expressions is a fundamental skill. One way to simplify expressions is by using the rules of exponents. Let's explore how to simplify the expression (3x²y)⁵.
Understanding the Rules of Exponents
To understand how to simplify this expression, we need to recall the following rules of exponents:
- Product of powers: (a^m)(a^n) = a^(m+n)
- Power of a product: (ab)^n = a^n b^n
- Power of a power: (a^m)^n = a^(m*n)
Simplifying the Expression
-
Apply the power of a product rule: (3x²y)⁵ = 3⁵ (x²)⁵ y⁵
-
Apply the power of a power rule: 3⁵ (x²)⁵ y⁵ = 3⁵ x¹⁰ y⁵
-
Calculate 3⁵: 3⁵ x¹⁰ y⁵ = 243x¹⁰ y⁵
Conclusion
Therefore, the simplified form of (3x²y)⁵ is 243x¹⁰ y⁵. This process demonstrates how to effectively simplify expressions involving exponents by applying the appropriate rules.