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

Previous problemNext problem

1:43 minutes

Problem 19

Textbook Question

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible.(xy)^4/7

Verified step by step guidance

Identify the expression given: \((xy)^{\frac{4}{7}}\).

Recognize that the expression is in the form of a rational exponent, where the numerator is the power and the denominator is the root.

Rewrite the expression using radical notation: \(\sqrt[7]{(xy)^4}\).

Simplify the expression inside the radical, if possible. In this case, \((xy)^4\) can be expanded to \(x^4y^4\).

The expression in radical form is \(\sqrt[7]{x^4y^4}\).

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Key Concepts

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

Radical Notation

Radical notation is a way to express roots of numbers or expressions using the radical symbol (√). For example, the square root of a number 'a' is written as √a. In algebra, radical notation can also represent fractional exponents, where the denominator indicates the root and the numerator indicates the power. Understanding this notation is essential for rewriting expressions involving roots.

Exponents and Fractional Exponents

Exponents represent repeated multiplication of a base number. A fractional exponent, such as 4/7, indicates both a root and a power: the denominator (7) signifies the root, while the numerator (4) indicates the exponent applied after taking the root. For instance, a^(m/n) can be rewritten as the nth root of a raised to the m power, which is crucial for simplifying expressions involving exponents.

Simplifying Expressions

Simplifying expressions involves reducing them to their simplest form, making them easier to work with. This can include combining like terms, reducing fractions, and applying the laws of exponents and radicals. In the context of the given expression, simplifying may involve rewriting it in a more manageable form using radical notation and ensuring that all components are expressed clearly and concisely.