Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 5 - Number Theory and the Real Number System - 5.6 Exponents and Scientific Notation - Exercise Set 5.6 - Page 321: 121

Answer

The solution of the given exponential expression is \[{{5}^{6}}\].

Work Step by Step

The quotient rule is defined as when an exponential is divided by another exponential expression of the same base, then subtract the exponent in the denominator from the exponent in the numerator and use this difference as the exponent of common base. Let \[{{a}^{m}}\] and \[{{a}^{n}}\] be two exponential expressions, then \[\frac{{{a}^{m}}}{{{a}^{n}}}\] can be expressed as \[\frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}}\] In the same way, express the provided expression: \[\begin{align} & \frac{{{5}^{8}}}{{{5}^{2}}}={{5}^{8-2}} \\ & ={{5}^{6}} \end{align}\] Hence, the quotient rule for exponentials can be understood with the help of this example.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.