(-3x^3y^2)(5xy^-1)

2 min read Jun 16, 2024

Multiplying Monomials: (-3x^3y^2)(5xy^-1)

This article will guide you through the process of multiplying the monomials (-3x^3y^2) and (5xy^-1).

Understanding Monomials

Monomials are algebraic expressions consisting of a single term, which can be a number, a variable, or a product of numbers and variables. The exponents of the variables in a monomial must be non-negative integers.

The Rules of Exponents

To multiply monomials, we utilize the following rules of exponents:

Product of Powers: When multiplying exponents with the same base, add the powers. x^m * x^n = x^(m+n)
Power of a Product: When raising a product to a power, raise each factor to that power. (xy)^n = x^n * y^n
Power of a Quotient: When raising a quotient to a power, raise both the numerator and denominator to that power. (x/y)^n = x^n / y^n

Multiplying the Monomials

Rearrange the terms: (-3x^3y^2)(5xy^-1) = (-3 * 5) * (x^3 * x) * (y^2 * y^-1)
Apply the Product of Powers rule: (-3 * 5) * (x^(3+1)) * (y^(2-1))
Simplify: -15x^4y

Conclusion

Therefore, the product of (-3x^3y^2) and (5xy^-1) is -15x^4y. By understanding the rules of exponents, we can efficiently multiply monomials.