Simplifying (6xy^5)^3
In mathematics, simplifying expressions is a crucial skill. One common type of simplification involves expressions raised to a power, such as (6xy^5)^3. Let's break down how to simplify this expression:
Understanding the Rules
The key rule we need is the power of a product rule:
(ab)^n = a^n * b^n
This rule states that when raising a product to a power, we raise each factor in the product to that power.
Applying the Rule

Identify the factors: In our expression (6xy^5)^3, the factors are 6, x, and y^5.

Apply the power rule: We raise each factor to the power of 3.
 6^3 = 6 * 6 * 6 = 216
 x^3 = x^3
 (y^5)^3 = y^(5*3) = y^15

Multiply the results: Now we multiply the simplified factors together.
 216 * x^3 * y^15 = 216x^3y^15
Conclusion
Therefore, the simplified form of (6xy^5)^3 is 216x^3y^15.