/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 121 Explain the quotient rule for ex... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 5: Problem 121

Explain the quotient rule for exponents. Use \(\frac{5^{8}}{5^{2}}\) in your explanation.

Short Answer

Expert verified
The simplified form of \(\frac{5^{8}}{5^{2}}\) is \(5^{6}\). This is in line with the quotient rule for exponents, which establishes that for like bases, the exponents are subtracted when divided.

Step by step solution

01

Setting Up the Quotient Rule Equation

Write down the quotient rule formula, which is \(a^{m} \div a^{n} = a^{m-n}\). This rule tells that when you divide like bases, you subtract the exponents.
02

Substitution of the Values

Replace the variables \(a\), \(m\), and \(n\) with the given values in the exercise. It will be: \(5^{8} \div 5^{2}\) which simplifies to \(5^{8-2}\).
03

Simplify the Expression

Perform the subtraction operation in the exponent \((8 - 2)\) to simplify the expression. The final simplified form will be: \(5^{6}\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=\frac{1}{5}, r=\frac{1}{2}\)

You are offered a job that pays $$\$ 30,000$$ for the first year with an annual increase of \(5 \%\) per year beginning in the second year. That is, beginning in year 2 , your salary will be \(1.05\) times what it was in the previous year. What can you expect to earn in your sixth year on the job? Round to the nearest dollar.

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,-6,-18,-30, \ldots\)

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=12, r=\frac{1}{2}\).
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.