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

Exponents

College Algebra

0. Review of Algebra

Exponents

1:52 minutes

Problem 86c

Textbook Question

Evaluate each expression. (-2)^5

Verified step by step guidance

Identify the base and the exponent in the expression \((-2)^5\). Here, the base is \(-2\) and the exponent is \(5\).

Understand that the exponent \(5\) indicates that the base \(-2\) should be multiplied by itself a total of 5 times.

Write out the multiplication: \((-2) \times (-2) \times (-2) \times (-2) \times (-2)\).

Calculate the product step by step, starting with the first two numbers: \((-2) \times (-2) = 4\).

Continue multiplying the result by the next \(-2\) until all factors are used: \(4 \times (-2)\), then \(-8 \times (-2)\), and so on.

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Key Concepts

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

Exponents

Exponents represent the number of times a base is multiplied by itself. In the expression (-2)^5, the base is -2, and the exponent is 5, indicating that -2 should be multiplied by itself five times. Understanding how to apply exponents is crucial for evaluating expressions involving powers.

Negative Numbers

Negative numbers are values less than zero, and they can affect the outcome of mathematical operations, especially when raised to an exponent. In this case, raising a negative number to an odd exponent results in a negative product, which is essential to remember when evaluating expressions like (-2)^5.

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. When evaluating expressions, it is important to follow these rules, particularly when dealing with exponents, multiplication, and addition, to arrive at the correct answer.