## Simplifying Algebraic Expressions: (4xy)(2x²y)(3xy)³

This article will guide you through simplifying the algebraic expression (4xy)(2x²y)(3xy)³.

### Understanding the Expression

The expression involves the product of multiple terms with variables and exponents. Let's break it down:

**(4xy)**: This term represents the product of 4, x, and y.**(2x²y)**: This term represents the product of 2, x squared, and y.**(3xy)³**: This term represents the cube of the product of 3, x, and y.

### Simplifying the Expression

To simplify the expression, we can follow these steps:

**Expand the Cube:**(3xy)³ is the same as (3xy)(3xy)(3xy)**Combine Coefficients:**Multiply the numerical coefficients together: 4 * 2 * 3 * 3 * 3 = 216.**Combine Variables:**Multiply the variables together, adding their exponents: x * x² * x * x * x = x⁶ and y * y * y * y = y⁴.

### Final Result

After combining the coefficients and variables, we arrive at the simplified expression: **216x⁶y⁴**.

### Key Concepts

**Exponents:**x² means x multiplied by itself twice (x * x).**Order of Operations:**Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.**Multiplication of Variables:**When multiplying variables with exponents, add their exponents.

### Conclusion

By applying the rules of exponents and multiplication, we were able to simplify the complex algebraic expression (4xy)(2x²y)(3xy)³ into the much simpler form 216x⁶y⁴.