Match each equation in Column I with the correct first step for solving it in Column II. (x+5)^2/3 - (x+5)^1/3 - 6 = 0

Key Concepts

Exponents and Roots

Understanding exponents and roots is crucial for manipulating equations involving powers. In the given equation, (x+5) is raised to the power of 2/3 and 1/3, which indicates that we are dealing with both squaring and taking cube roots. Recognizing how to simplify these expressions will help in isolating the variable effectively.

Substitution

Substitution is a technique used to simplify complex expressions by replacing a variable or expression with a single variable. In this case, letting u = (x + 5)^(1/3) can transform the equation into a more manageable form, allowing for easier solving of the polynomial equation that results.

Factoring Polynomials

Factoring polynomials is a method used to break down complex polynomial expressions into simpler components that can be solved more easily. Once the equation is simplified through substitution, recognizing patterns or applying the quadratic formula can help in finding the roots of the resulting polynomial equation.