Simplifying the Expression (4xy^2)(2y)^3
This article will guide you through the process of simplifying the algebraic expression (4xy^2)(2y)^3.
Understanding the Order of Operations
To simplify this expression, we need to follow the order of operations, commonly remembered by the acronym PEMDAS or BODMAS:
 Parentheses (or Brackets)
 Exponents (or Orders)
 Multiplication and Division (from left to right)
 Addition and Subtraction (from left to right)
Simplifying the Expression StepbyStep

Simplify the exponent:
 (2y)^3 = (2y) * (2y) * (2y) = 8y^3

Multiply the coefficients:
 4 * 8 = 32

Combine the variables:
 x * y^2 * y^3 = x * y^(2+3) = xy^5

Final result:
 (4xy^2)(2y)^3 = 32xy^5