(-4x%5E9y%5E2).jpeg "(-3x^5y)(-4x^9y^2)")
Multiplying Monomials: A Step-by-Step Guide
This article will guide you through multiplying the monomials (-3x^5y) and (-4x^9y^2). We'll break down the process into simple steps, making it easy to understand.
Understanding Monomials
Monomials are algebraic expressions consisting of a single term. This term can be a constant, a variable, or a product of constants and variables. For example, -3x^5y, -4x^9y^2, and 5 are all monomials.
Multiplying Monomials
To multiply monomials, we follow these steps:
- Multiply the coefficients: Multiply the numerical values in front of the variables.
- Multiply the variables: Multiply the variables together. Remember to use the rules of exponents: when multiplying variables with the same base, add their powers.
Applying the Steps to our Problem
Let's apply these steps to (-3x^5y)(-4x^9y^2):
- Multiply the coefficients: (-3) * (-4) = 12
- Multiply the variables:
- x^5 * x^9 = x^(5+9) = x^14
- y * y^2 = y^(1+2) = y^3
Final Result
Putting it all together, we get:
(-3x^5y)(-4x^9y^2) = 12x^14y^3
Therefore, the product of (-3x^5y) and (-4x^9y^2) is 12x^14y^3.