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

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:11 minutes

Problem 82

Textbook Question

Evaluate each expression. -3^5

Verified step by step guidance

Identify the base and the exponent in the expression \(-3^5\).

Recognize that the expression \(-3^5\) means \(-(3^5)\), not \((-3)^5\).

Calculate the power of 3 raised to 5, which is \(3^5\).

Apply the negative sign to the result of \(3^5\) to get \(-(3^5)\).

Understand that the negative sign is applied after the exponentiation.

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Key Concepts

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

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. The exponent indicates how many times the base is multiplied by itself. For example, in the expression 3^5, 3 is the base and 5 is the exponent, meaning 3 is multiplied by itself five times: 3 × 3 × 3 × 3 × 3.

Order of Operations

The order of operations is a set of rules that dictates the sequence in which mathematical operations should be performed to ensure consistent results. The common acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) helps remember this order. In the expression -3^5, the exponentiation is performed before applying the negative sign.

Negative Numbers and Exponents

When dealing with negative numbers and exponents, it is crucial to understand how the negative sign interacts with the exponent. In the expression -3^5, the negative sign is not included in the exponentiation, meaning it evaluates as -(3^5). This results in a negative outcome, as the base (3) is raised to the power of 5 first, and then the negative sign is applied.