When using the Product Property to simplify the expression ${} (3u^{-5}v^7)(-4u^4v^{-2})$, which of the following describes the correct first steps for handling the numerical coefficients and the exponents of the variable $u$?

An engineer is optimizing a data processing script that simplifies the algebraic expression $(2x^{-6}y^8)(-5x^5y^{-3})$. True or False: According to the Product Property of Exponents, the numerical coefficients ${}2$ and $-5$ should be multiplied together, while the exponents of the $x$ variables ($-6$ and $5$) should be added together.

A laboratory technician is simplifying an algebraic model represented by the expression $(2x^{-6}y^8)(-5x^5y^{-3})$. Arrange the following steps in the correct order to simplify this expression using the Product Property of Exponents.

A logistics coordinator is using a spreadsheet model to calculate packaging efficiency, which involves simplifying the algebraic expression $(2x^{-6}y^8)(-5x^5y^{-3})$. After grouping like terms, multiplying the coefficients, and adding the exponents, the coordinator arrives at an intermediate result of $-10x^{-1}y^5$. To express the final answer with only positive exponents, the $x^{-1}$ term must be relocated to the ________ of the fraction.

Rules for Simplifying Algebraic Models in Production

Simplifying Route Optimization Formula