Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 14: Problem 17

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. \(\left(4^{4}\right)\left(10^{4}\right)\)

Short Answer

Expert verified
The answer is option 'a', which is \(10^{6}\).

Step by step solution

01

Solve for x

Given the equation \(4^{x}=1,024\), find the value of \(x\) by expressing 1,024 as a base 4 expression. We have that \(4^{5} = 1,024\), so we conclude that \(x=5\).
02

Substitute x in the expression

Having obtained \(x=5\), substitute this into the expression \(\left(4^{x+1}\right)\left(5^{x-1}\right)\) replacing \(x\) with 5. This gives us:\(\left(4^{5+1}\right)\left(5^{5-1}\right)=\left(4^{6}\right)\left(5^{4}\right)\)
03

Perform exponent calculations

Calculate the value of each exponent i.e. \(\left(4^{6}\right)\) and \(\left(5^{4}\right)\). This simplifies our expression to \(\left(4,096\right)\left(625\right)\)
04

Multiply the calculated values

Now, multiply \(4,096\) by \(625\). This gives us a final value of \(2,560,000\).
05

Match the result with the options

The last step is to compare this result, \(2,560,000\), with the options given. \(2,560,000\) is equal to \(10^{6}\).

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.

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

\(x \neq 0\) Quantity \(\mathbf{A}\) \(\frac{x}{10}\) Quantity \(\mathbf{B}\) \(\frac{\frac{x}{5}}{2}\) 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.

Joe has \(\$ 200\). If he buys a CD player for \(\$ 150,\) what is the greatest number of CDs he can buy with the remaining money if CDs cost \(\$ 12\) each?

If 16 is the average (arithmetic mean) of \(p, 24,\) and \(q,\) what is \(16(p+q) ?\) a. 180 b. 192 c. 384 d. 524 e. 768

If \(|2 x-3|+2>7,\) which of the following could be the value of \(x ?\) Indicate all such values. a. -4 b. -3 c. -2 d. -1 e. 0 f. 1 g. 2 h. 3

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
See all solutions

Recommended explanations on English Textbooks

Listening and Speaking

Read Explanation

English Grammar Summary

Read Explanation

History of English Language

Read Explanation

Graphology

Read Explanation

Linguistic Terms

Read Explanation

Essay Prompts

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