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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0:29 minutes

Problem 71

Textbook Question

Find each product or quotient where possible. 0/-8

Verified step by step guidance

Identify the operation: The problem involves division, specifically dividing 0 by -8.

Recall the rule for division involving zero: Any number divided by zero is undefined, but zero divided by any non-zero number is zero.

Apply the rule: Since 0 is being divided by -8, and -8 is a non-zero number, the result of the division is 0.

Understand the concept: Dividing zero by any non-zero number always results in zero because zero represents the absence of quantity.

Conclude the process: The division of 0 by -8 is valid and results in 0.

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Key Concepts

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

Division by Zero

In mathematics, division by zero is undefined. This means that any expression where the divisor is zero does not yield a valid numerical result. In the case of the expression 0/-8, the divisor is -8, which is not zero, allowing for a valid division. However, if the divisor were zero, the operation would be invalid.

Zero as a Numerator

When zero is the numerator in a fraction, the result is always zero, provided the denominator is not zero. This is because zero divided by any non-zero number equals zero. In the expression 0/-8, the numerator is zero, leading to a result of zero, which is a fundamental property of division involving zero.

Negative Numbers in Division

Dividing by a negative number affects the sign of the result. When a positive number is divided by a negative number, the result is negative. In the expression 0/-8, since the denominator is negative, the result remains zero, as zero does not change sign regardless of the sign of the denominator.