Simplifying Algebraic Expressions: (5m^9)(7m^3n^7)+(2m^2n^6)(m^10n)
This article will guide you through simplifying the algebraic expression (5m^9)(7m^3n^7)+(2m^2n^6)(m^10n).
Understanding the Rules
To simplify this expression, we need to understand the following rules:
 Product of powers: When multiplying exponents with the same base, you add the powers. For example, x^a * x^b = x^(a+b).
 Commutative property of multiplication: The order of multiplication doesn't affect the result. For example, a * b = b * a.
Simplifying the Expression

Distribute: We start by distributing the multiplication:
 (5m^9)(7m^3n^7) = 35m^(9+3)n^7 = 35m^12n^7
 (2m^2n^6)(m^10n) = 2m^(2+10)n^(6+1) = 2m^12n^7

Combine like terms: Now we have: 35m^12n^7 + 2m^12n^7

Simplify: Since the terms have the same variables and exponents, we can combine their coefficients: (35 + 2)m^12n^7 = 37m^12n^7
The Simplified Expression
Therefore, the simplified form of (5m^9)(7m^3n^7)+(2m^2n^6)(m^10n) is 37m^12n^7.