(8x^2y)(x^4y^3)^2

Jasonbradley

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Jun 16, 2024

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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).

Step-by-Step Simplification

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

2. 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.