Simplifying Algebraic Expressions: (5x^3y)^2(2x^5y^1)
This article will guide you through the process of simplifying the algebraic expression (5x^3y)^2(2x^5y^1).
Understanding the Rules
Before we begin, let's recall some essential rules of exponents:
 Power of a product: (ab)^n = a^n * b^n
 Power of a power: (a^m)^n = a^(m*n)
 Product of powers: a^m * a^n = a^(m+n)
StepbyStep Simplification

Simplify the first term:
 (5x^3y)^2 = 5^2 * (x^3)^2 * y^2 = 25x^6y^2

Simplify the second term:
 (2x^5y^1) remains as it is.

Multiply the simplified terms:
 25x^6y^2 * (2x^5y^1) = 50x^(6+5)y^(2+1)

Combine the exponents:
 50x^(6+5)y^(2+1) = 50x^11y^3
Final Result
Therefore, the simplified form of the expression (5x^3y)^2(2x^5y^1) is 50x^11y^3.
Key Points
 Remember the order of operations (PEMDAS/BODMAS) when dealing with expressions.
 Pay close attention to the signs of the coefficients.
 Always simplify expressions to their simplest form.