Simplifying (6xy^5)^3
This expression involves raising a product of terms to a power. Let's break down how to simplify it:
Understanding the Rules
 Power of a product: When a product is raised to a power, each factor within the product is raised to that power.
 (ab)^n = a^n * b^n
 Power of a power: When a power is raised to another power, the exponents are multiplied.
 (a^m)^n = a^(m*n)
Applying the Rules
Let's apply these rules to (6xy^5)^3:

Apply the power of a product rule: (6xy^5)^3 = 6^3 * x^3 * (y^5)^3

Apply the power of a power rule: 6^3 * x^3 * (y^5)^3 = 6^3 * x^3 * y^(5*3)

Simplify the exponents: 6^3 * x^3 * y^(5*3) = 216 * x^3 * y^15
Final Answer
Therefore, the simplified form of (6xy^5)^3 is 216x^3y^15.