(5ab%5E4c%5E2).jpeg "(-7a^4bc^3)(5ab^4c^2)")
Multiplying Monomials: A Step-by-Step Guide
This article will guide you through the process of multiplying the monomials (-7a⁴bc³) (5ab⁴c²).
Understanding Monomials
Monomials are algebraic expressions that consist of a single term. They are formed by multiplying constants and variables raised to non-negative integer exponents. In our case, we have two monomials:
- -7a⁴bc³: This monomial has a coefficient of -7 and variables a, b, and c raised to the powers of 4, 1, and 3, respectively.
- 5ab⁴c²: This monomial has a coefficient of 5 and variables a, b, and c raised to the powers of 1, 4, and 2, respectively.
The Multiplication Process
To multiply monomials, we follow these steps:
- Multiply the coefficients: -7 * 5 = -35
- Multiply the variables with the same base by adding their exponents:
- a⁴ * a¹ = a⁵ (4 + 1 = 5)
- b¹ * b⁴ = b⁵ (1 + 4 = 5)
- c³ * c² = c⁵ (3 + 2 = 5)
The Final Result
Combining the results from steps 1 and 2, we get the final product:
(-7a⁴bc³) (5ab⁴c²) = -35a⁵b⁵c⁵
Key Points to Remember
- Coefficients: Multiply the coefficients together.
- Variables: Multiply variables with the same base by adding their exponents.
- Exponents: The exponents of the variables in the product are the sum of their respective exponents in the original monomials.