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

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

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2:01 minutes

Problem 63

Textbook Question

Use the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜m/n⁴

Verified step by step guidance

Identify the expression: \( \sqrt[4]{\frac{m}{n^4}} \).

Apply the property of radicals: \( \sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}} \).

Rewrite the expression as \( \frac{\sqrt[4]{m}}{\sqrt[4]{n^4}} \).

Simplify \( \sqrt[4]{n^4} \) using the property \( \sqrt[n]{a^n} = a \), which gives \( n \).

The expression simplifies to \( \frac{\sqrt[4]{m}}{n} \).

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Key Concepts

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

Radical Expressions

Radical expressions involve roots, such as square roots, cube roots, and higher-order roots. The expression ∜m/n⁴ represents the fourth root of the fraction m/n⁴. Understanding how to manipulate these expressions is crucial for simplifying and performing operations on them.

Properties of Exponents

The properties of exponents govern how to simplify expressions involving powers. For instance, when dividing like bases, you subtract the exponents. In the context of radicals, the relationship between roots and exponents is essential, as the nth root of a number can be expressed as that number raised to the power of 1/n.

Simplifying Radicals

Simplifying radicals involves rewriting a radical expression in its simplest form. This includes factoring out perfect squares, cubes, or higher powers from under the radical sign. For the expression ∜m/n⁴, recognizing how to separate the numerator and denominator and simplify each part is key to performing the indicated operations correctly.