Factor out the least power of the variable or variable expression. Assume all variables represent positive real numbers. See Example 8. (3r+1)^-2/3+(3r+1)^1/3+(3r+1)^4/3

Key Concepts

Factoring Expressions

Factoring involves rewriting an expression as a product of its factors. In the context of algebra, this often means identifying common terms or variables in each part of the expression. By factoring out the least power of a variable or expression, we simplify the problem, making it easier to manipulate and solve.

Exponents and Powers

Exponents represent repeated multiplication of a base number. Understanding how to manipulate exponents, including the rules for adding, subtracting, and multiplying powers, is crucial for simplifying expressions. In this question, recognizing the least power of the variable expression helps in the factoring process.

Combining Like Terms

Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This concept is essential when working with polynomials or expressions involving exponents, as it allows for a more straightforward representation of the expression after factoring.