Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 10

By which of the following could \(10\left(9^{6}\right)\) be divided by to produce an integer result? Indicate all such values. a. 90 b. 100 c. 330 d. 540 e. 720

Short Answer

Expert verified
After analyzing, it's found that \(10\left(9^{6}\right)\) could be divided perfectly by 100 and 540.

Step by step solution

01

Calculate \(10(9^6)\)

Begin by calculating the value of \(10\left(9^{6}\right)\). Use the exponent law that says \(a^{m} * a^{n} = a^{m+n}\) to simplify \(9^{6}\). After this, multiply the resulting value by 10 to find the ultimate value.
02

Check for divisibility

Now that you have the value of \(10\left(9^{6}\right)\), the next step will be to determine which of the given number(s) can divide the computed value perfectly (i.e., without any remainder). Do this by taking each option one after another and use it to divide \(10\left(9^{6}\right)\). A number that results in a whole quotient and zero remainder will be a suitable divisor. To save time, start by trying to factorize the options. Any number that has a factor also present in the factorization of \(10(9^6)\) could be a potential correct divisor.
03

Confirming the Answers

After finding all the numbers that could divide \(10\left(9^{6}\right)\) perfectly, list them as the answer(s). Remember, there could be more than one correct answer.

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

If three boys and three girls sit in a row on a park bench, and no boy can sit on either end of the bench, how many arrangements of the children on the bench are possible? a. 46,656 b. 38,880 c. 1,256 d. 144 e. 38

If \(4^{x}=1,024,\) then \(\left(4^{x}+1\right)\left(5^{x-1}\right)=\) a. \(10^{6}\) b. \(\left(5^{4}\right)\left(10^{5}\right)\) c. \(\left(4^{4}\right)\left(10^{5}\right)\) d. \(\left(5^{4}\right)\left(10^{4}\right)\) e. \(\left(4^{4}\right)\left(10^{4}\right)\)

What is the greatest distance between two vertices of a rectangular solid with a height of \(5,\) a length of \(12,\) and a volume of \(780 ?\) a. 12 b. \(12 \sqrt{2}\) c. 13 d. \(13 \sqrt{2}\) e. \(13 \sqrt{3}\)

Quantity \(\mathbf{A}\) The greatest odd factor of 78 Quantity \(\mathbf{B}\) The greatest prime factor of 78 a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal d. The relationship cannot be determined from the information given.

The test scores for a class have a normal distribution, a mean of \(50,\) and a standard deviation of 4. Quantity \(\mathbf{A}\) Percentage of scores at or above 58 Quantity \(\mathbf{B}\) Percentage of scores at or below 42 a. Quantity A is greater b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.
See all solutions

Recommended explanations on English Textbooks

Pragmatics

Read Explanation

Sociolinguistics

Read Explanation

Language and Social Groups

Read Explanation

Language Analysis

Read Explanation

Essay Prompts

Read Explanation

Multiple Choice Questions

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.

Sign-up for free