%5E2.jpeg "(3xy^3)^2")
Simplifying (3xy^3)^2
In mathematics, simplifying expressions is a fundamental skill. Let's explore how to simplify the expression (3xy^3)^2.
Understanding the Concept
The expression (3xy^3)^2 represents the product of the term (3xy^3) multiplied by itself. In essence, we are squaring the entire expression inside the parentheses.
Applying the Rules
To simplify this expression, we need to apply the following rules of exponents:
- Product of Powers: (a^m)^n = a^(m*n)
- Power of a Product: (ab)^n = a^n * b^n
Simplifying the Expression
- Apply the power of a product rule: (3xy^3)^2 = 3^2 * x^2 * (y^3)^2
- Apply the product of powers rule: 3^2 * x^2 * (y^3)^2 = 9x^2 * y^(3*2)
- Simplify: 9x^2 * y^(3*2) = 9x^2y^6
Conclusion
Therefore, the simplified form of (3xy^3)^2 is 9x^2y^6. This simplification process demonstrates the importance of understanding and applying the fundamental rules of exponents.