Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. 9z^-1/2+2z^1/2

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In algebra, this often involves identifying common terms or expressions that can be extracted from a polynomial or algebraic expression, simplifying the problem and making it easier to solve.

Exponents represent repeated multiplication of a base number. In the expression 9z^-1/2 + 2z^1/2, the exponents indicate the power to which the variable z is raised. Understanding how to manipulate exponents, including the rules for multiplying and dividing powers, is essential for simplifying expressions and performing operations on them.

A common factor is a term that appears in each part of an expression, which can be factored out to simplify the expression. In the given example, identifying the least power of the variable z allows for the extraction of z^-1/2 from both terms, leading to a more manageable expression. This technique is crucial for simplifying algebraic expressions and solving equations.