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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1:50 minutes

Problem 84

Textbook Question

Evaluate each expression. (-2)^6

Verified step by step guidance

Identify the base and the exponent in the expression \((-2)^6\). The base is \(-2\) and the exponent is 6.

Understand that the exponent indicates how many times the base is multiplied by itself. So, \((-2)^6\) means \((-2) \times (-2) \times (-2) \times (-2) \times (-2) \times (-2)\).

Calculate the product step by step: First, multiply the first two terms: \((-2) \times (-2) = 4\).

Continue multiplying the result by the next \(-2\): \(4 \times (-2) = -8\).

Repeat this process until all terms are multiplied: \(-8 \times (-2) = 16\), \(16 \times (-2) = -32\), \(-32 \times (-2) = 64\).

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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)^6, the base is -2, and the exponent is 6, indicating that -2 should be multiplied by itself six times. Understanding how to apply exponents is crucial for evaluating expressions involving powers.

Negative Base

When dealing with a negative base raised to an even exponent, the result is positive. In this case, (-2)^6 results in a positive value because multiplying an even number of negative factors yields a positive product. Recognizing the behavior of negative bases in exponentiation is essential for accurate calculations.

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. In evaluating (-2)^6, it is important to follow these rules, which prioritize exponentiation before multiplication or addition, ensuring the expression is simplified correctly.