/*! 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 29 Simplify. \(\frac{r^{4}\left(r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 29

Simplify. \(\frac{r^{4}\left(r^{5}\right)^{7}}{2 t\left(11 t^{2}\right)^{2}}\)

Short Answer

Expert verified
The simplified expression is \(\frac{r^{39}}{242t^5}\).

Step by step solution

01

Simplify the numerator

In the numerator, expand the expression \((r^5)^7\). By applying the power-to-power rule (when an exponent is raised to another exponent, we multiply the exponents), we get: \(r^{4} \cdot r^{35}\).
02

Combine the r terms in the numerator

Next, combine the r terms in the numerator. According to the product rule for exponents, we add the exponents when the bases are the same: \(r^{4+35} = r^{39}\).
03

Simplify the denominator

In the denominator, expand the expression \((11t^2)^2\). By applying the power-to-power rule, we find that the expression becomes: \(11^2 \cdot t^{2\cdot 2} = 121 \cdot t^4\).
04

Multiply the denominator

Multiply the terms in the denominator: \(2t \cdot 121t^4 = 242t^{1+4} = 242t^5\).
05

Write the simplified fraction

Finally, write the simplified expression as a fraction: \(\frac{r^{39}}{242t^5}\). So, the simplified expression is: \[ \frac{r^{39}}{242t^5} \]

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

Simplify using the quotient rule. $$\frac{15 w^{2}}{w^{10}}$$

Simplify using the quotient rule. $$\frac{-8 p^{5}}{p^{15}}$$

Simplify the expression using the product rule. Leave your answer in exponential form. $$5^{2} \cdot 5^{3} \cdot 5^{4}$$

Simplify the expression using one of the power rules. $$\left(\frac{d}{c}\right)^{8}$$

Perform the operation as indicated. Write the final answer without an exponent. \(\left(3.19 \times 10^{-5}\right)+\left(9.2 \times 10^{-5}\right)\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

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.