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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1:57 minutes

Problem 33

Textbook Question

In Exercises 25–34, use the zero-exponent rule to simplify each expression.(13y)⁰

Verified step by step guidance

Identify the zero-exponent rule, which states that any non-zero number raised to the power of zero is equal to 1.

Recognize that the expression \((13y)^0\) involves raising the entire term \(13y\) to the power of zero.

Apply the zero-exponent rule to the expression \((13y)^0\).

Conclude that the expression simplifies to 1, as any non-zero base raised to the zero power is 1.

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Key Concepts

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

Zero Exponent Rule

The zero exponent rule states that any non-zero base raised to the power of zero equals one. This rule is fundamental in algebra as it simplifies expressions significantly. For example, (13y)⁰ simplifies to 1, regardless of the values of 13 and y, as long as they are not zero.

Exponential Notation

Exponential notation is a way to express repeated multiplication of a number by itself. In the expression (13y)⁰, the base is 13y, and the exponent indicates how many times the base is multiplied. Understanding this notation is crucial for applying the zero exponent rule correctly.

Non-zero Bases

In the context of the zero exponent rule, it is important to note that the base must be non-zero. If the base is zero, the expression 0⁰ is considered indeterminate in mathematics. Therefore, when applying the zero exponent rule, ensuring the base is not zero is essential for valid simplification.