(-2x%5E3y%5E4).jpeg "(-7x^2y^4)(-2x^3y^4)")
Multiplying Monomials: (-7x²y⁴)(-2x³y⁴)
This article will guide you through multiplying the monomials (-7x²y⁴)(-2x³y⁴). We'll break down the process step by step, covering the key concepts involved.
Understanding Monomials
A monomial is a single term algebraic expression that consists of a coefficient (a number), one or more variables, and possibly exponents. For example, -7x²y⁴ and -2x³y⁴ are both monomials.
Multiplying Monomials
To multiply monomials, we follow these steps:
- Multiply the coefficients: In our case, we multiply -7 and -2, resulting in 14.
- Multiply the variables: We combine the variables with the same base by adding their exponents. For the variable 'x', we add 2 and 3, getting x⁵. For the variable 'y', we add 4 and 4, resulting in y⁸.
Applying the Steps
Let's apply these steps to our problem:
(-7x²y⁴)(-2x³y⁴) = ( -7 * -2 ) ( x² * x³ ) ( y⁴ * y⁴ ) = 14x⁵y⁸
Conclusion
Therefore, the product of (-7x²y⁴) and (-2x³y⁴) is 14x⁵y⁸. This example demonstrates the straightforward process of multiplying monomials, which involves multiplying coefficients and combining variables with the same base by adding their exponents.