Simplifying the Expression (7x^2y^3)(3x^5y^8)
This expression involves multiplying monomials. Monomials are algebraic expressions that consist of a single term, which is a product of constants, variables, and possibly positive integer exponents. To simplify this expression, we use the following rules:
 Product of powers: When multiplying powers with the same base, add the exponents. For example, x^m * x^n = x^(m+n)
 Commutative property: The order of multiplication does not affect the result. For example, a * b = b * a
Let's break down the simplification stepbystep:

Rearrange the terms: (7x^2y^3)(3x^5y^8) = 7 * 3 * x^2 * x^5 * y^3 * y^8

Apply the product of powers rule: 7 * 3 * x^2 * x^5 * y^3 * y^8 = 21 * x^(2+5) * y^(3+8)

Simplify the exponents: 21 * x^(2+5) * y^(3+8) = 21x^7y^11
Therefore, the simplified form of (7x^2y^3)(3x^5y^8) is 21x^7y^11.