Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Radical Expressions

College Algebra

0. Review of Algebra

Radical Expressions

1:12 minutes

Problem 26d

Textbook Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x^5)^5

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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 power of a product ( (ab)^n = a^n * b^n). Understanding these rules is essential for simplifying expressions with exponents.

Negative Exponents

Negative exponents indicate the reciprocal of the base raised to the opposite positive exponent. For example, a^(-n) = 1/(a^n). This concept is crucial when simplifying expressions that may involve negative powers, ensuring that all terms are expressed in a standard form.

Polynomial Expressions

Polynomial expressions are algebraic expressions that consist of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication. In the given expression, (-2x^5)^5, recognizing it as a polynomial allows for the application of exponent rules to simplify it effectively.