Simplifying the Expression (6n^5)(3n^3)^2
This article aims to explain the process of simplifying the algebraic expression (6n^5)(3n^3)^2. We will use the properties of exponents to achieve this.
Understanding the Properties of Exponents
To simplify the expression, we need to understand the following properties of exponents:
 Product of powers: x^m * x^n = x^(m+n)
 Power of a product: (xy)^n = x^n * y^n
 Power of a power: (x^m)^n = x^(m*n)
Simplifying the Expression

Simplify the exponent:
 (3n^3)^2 = 3^2 * (n^3)^2 = 9n^6

Apply the product of powers rule:
 (6n^5) * (9n^6) = 6 * 9 * n^(56)

Simplify the multiplication:
 54 * n^11

Express the negative exponent in the denominator:
 54 / n^11
Conclusion
Therefore, the simplified form of the expression (6n^5)(3n^3)^2 is 54 / n^11.