In Exercises 1–8, multiply the monomials. (−3xy²z⁵)(2xy⁷z⁴)

Key Concepts

Monomials

A monomial is a polynomial with only one term, which can be a constant, a variable, or a product of constants and variables raised to non-negative integer powers. In the given question, both (−3xy²z⁵) and (2xy⁷z⁴) are monomials, and understanding their structure is essential for multiplication.

Multiplication of Monomials

When multiplying monomials, you multiply the coefficients (numerical parts) and then apply the laws of exponents to the variables. Specifically, you add the exponents of like bases. This process is crucial for simplifying the product of the two given monomials.

Laws of Exponents

The laws of exponents govern how to handle operations involving powers of numbers and variables. Key rules include that when multiplying like bases, you add the exponents, and when raising a power to a power, you multiply the exponents. These rules are vital for correctly simplifying the result of the multiplication in the exercise.