Simplifying the Expression: (8x^2y)(x^4y^3)^2
This expression involves multiplying monomials, a fundamental concept in algebra. Here's how to simplify it:
Understanding the Rules
 Exponents: When raising a power to another power, you multiply the exponents. For example, (x^m)^n = x^(m*n).
 Multiplication: When multiplying monomials, you multiply the coefficients and add the exponents of the same variables. For example, (a^m * a^n) = a^(m+n).
StepbyStep Simplification

Simplify the exponent: (x^4y^3)^2 = x^(42) * y^(32) = x^8y^6

Multiply the monomials: (8x^2y)(x^8y^6) = 8 * x^(2+8) * y^(1+6) = 8x^10y^7
Final Result:
The simplified form of the expression (8x^2y)(x^4y^3)^2 is 8x^10y^7.