Simplifying (x^2y^3)^3
In mathematics, simplifying expressions is a crucial skill. One common type of expression involves exponents raised to another exponent. Let's explore how to simplify the expression (x^2y^3)^3.
Understanding the Rules of Exponents
The key to simplifying this expression lies in understanding the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents:
(a^m)^n = a^(m*n)
Applying the Rule
Let's break down the simplification process step by step:

Identify the base and exponents: In our expression (x^2y^3)^3, the base is (x^2y^3) and the exponent is 3.

Apply the power of a power rule: We multiply the exponents of each term within the parentheses by the outer exponent:
(x^2y^3)^3 = x^(23) y^(33)

Simplify:
x^(23) y^(33) = x^6 y^9
Final Result
Therefore, the simplified form of (x^2y^3)^3 is x^6y^9.
Importance of Understanding Exponent Rules
Mastering exponent rules is crucial for simplifying complex expressions and solving various mathematical problems. By understanding these rules, you can confidently navigate expressions with multiple exponents and simplify them effectively.