Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Rational Exponents

College Algebra

0. Review of Algebra

Rational Exponents

Previous problemNext problem

1:24 minutes

Problem 179

Textbook Question

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?

Verified step by step guidance

Substitute \(-8\) for \(x\) in the equation: \(5(-8)^{2/3} + 11(-8)^{1/3} + 2 = 0\).

Calculate \((-8)^{1/3}\), which is the cube root of \(-8\).

Calculate \((-8)^{2/3}\), which is the square of the cube root of \(-8\).

Substitute the values of \((-8)^{1/3}\) and \((-8)^{2/3}\) back into the equation.

Simplify the expression to see if it equals zero.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.