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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1:20 minutes

Problem 30

Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2

Verified step by step guidance

Identify the expression to simplify: \((p^4/q)^2\).

Apply the power of a quotient rule: \((a/b)^n = a^n/b^n\).

Raise both the numerator and the denominator to the power of 2: \((p^4)^2/(q)^2\).

Apply the power of a power rule to the numerator: \((p^4)^2 = p^{4 \times 2} = p^8\).

The simplified expression is \(p^8/q^2\).

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Key Concepts

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

Exponent Rules

Exponent rules are fundamental principles that govern how to manipulate expressions involving powers. Key rules include the product of powers (a^m * a^n = a^(m+n)), the power of a power ((a^m)^n = a^(m*n)), and the quotient of powers (a^m / a^n = a^(m-n)). Understanding these rules is essential for simplifying expressions with exponents.

Simplifying Rational Expressions

Simplifying rational expressions involves reducing fractions to their simplest form by canceling common factors in the numerator and denominator. This process often requires factoring polynomials and applying the rules of exponents to ensure that the expression is expressed in the most concise manner possible.

Nonzero Variables

In algebra, assuming that variables represent nonzero real numbers is crucial for avoiding undefined expressions, particularly in division. This assumption allows for the application of exponent rules without concern for division by zero, ensuring that the simplification process remains valid and applicable in real-world scenarios.