Exercises 177–179 will help you prepare for the material covered in the next section. If - 8 is substituted for x in the equation 5x^(2/3) + 11x^(1/3) + 2 = 0, is the resulting statement true or false?

Key Concepts

Exponents and Fractional Powers

Understanding exponents, particularly fractional powers, is crucial in algebra. The expression x^(2/3) represents the cube root of x squared, while x^(1/3) is the cube root of x. This knowledge allows students to manipulate and simplify expressions involving roots and powers effectively.

Substitution in Equations

Substitution involves replacing a variable in an equation with a specific value to evaluate the truth of the statement. In this case, substituting -8 for x in the equation allows us to determine if the left-hand side equals zero, which is essential for solving the equation.

Evaluating Polynomial Expressions

Evaluating polynomial expressions requires substituting values into the expression and performing arithmetic operations. This process helps in determining whether the expression equals zero, which is a key step in solving polynomial equations and understanding their roots.