Skip to main content
Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 137
Chapter 1, Problem 137

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛(8/x⁴)

Verified step by step guidance
1
Identify the expression given: \(\sqrt[3]{\frac{8}{x^4}}\) which means the cube root of the fraction \(\frac{8}{x^4}\).
Recall that the cube root of a fraction can be written as the fraction of the cube roots: \(\sqrt[3]{\frac{8}{x^4}} = \frac{\sqrt[3]{8}}{\sqrt[3]{x^4}}\).
Simplify the cube root of the numerator: since \(8 = 2^3\), \(\sqrt[3]{8} = 2\).
Rewrite the cube root of the denominator using exponent rules: \(\sqrt[3]{x^4} = x^{\frac{4}{3}}\) because the cube root is the same as raising to the power \(\frac{1}{3}\).
Combine the simplified numerator and denominator to write the expression as \(\frac{2}{x^{\frac{4}{3}}}\), which is the simplified form.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

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

Cube Roots and Radicals

A cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, ∛8 equals 2 because 2³ = 8. Understanding how to simplify cube roots is essential for manipulating expressions involving radicals.
Recommended video:
Guided course
05:20
Expanding Radicals

Properties of Exponents

Exponents indicate repeated multiplication of a base number. Key properties include the product rule, quotient rule, and power rule, which help simplify expressions with variables raised to powers. For example, x⁴ means x multiplied by itself four times.
Recommended video:
Guided course
04:06
Rational Exponents

Simplifying Algebraic Fractions

Simplifying algebraic fractions involves reducing expressions by factoring, canceling common terms, and applying exponent rules. When variables are in denominators with exponents, rewriting them using negative exponents or radicals can aid simplification.
Recommended video:
Guided course
05:07
Simplifying Algebraic Expressions
Related Practice
Textbook Question

Complete the table of fraction, decimal and percent equivalents.

Textbook Question

Use the distributive property to calculate each value mentally. 72∙17+28∙17

3
views
Textbook Question

Complete the table of fraction, decimal and percent equivalents. Fraction in lowest terms(or Whole Number) 1/3 Decimal ? Percent ?

Textbook Question

Factor each polynomial over the set of rational number coefficients. (25/9)x4-(9y2)

Textbook Question

Perform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. x5y3z2\(\sqrt{\frac{x^5y^3}{z^2}\)}

3
views
Textbook Question

Find all values of b or c that will make the polynomial a perfect square trinomial. 4z2+bz+81