![[m]\frac{1}{\frac{1}{\sqrt[3]{a+b}}}*\frac{\sqrt[3]{(a+b})^4}{\frac{1}](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "[m]\frac{1}{\frac{1}{\sqrt[3]{a+b}}}*\frac{\sqrt[3]{(a+b})^4}{\frac{1}"){kind=icon}
by: Archit3110
6 mins
Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 1808:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (01:45) correct
32%
(02:07)
wrong
based on 222
sessions
History
Date
Time
Result
Not Attempted Yet
\(\frac{1}{\frac{1}{\sqrt[3]{a+b}}}*\frac{\sqrt[3]{(a+b)^4}}{\frac{1}{(a+b)^{-\frac{2}{3}}}}=\)
(A) 1
(B) (a + b)-1/3
(C) (a + b)1/3
(D) (a + b)2/3
(E) a + b
Sorry about the image equation. Tried hard with latex to make this appear fine, but doesn't seem to be working out
(A) 1
(B) (a + b)-1/3
(C) (a + b)1/3
(D) (a + b)2/3
(E) a + b
Sorry about the image equation. Tried hard with latex to make this appear fine, but doesn't seem to be working out
Attachments
File comment: Equation
eqn.png [ 988 Bytes | Viewed 5371 times ]
rajarams
\(\frac{1}{\frac{1}{\sqrt[3]{a+b}}}*\frac{\sqrt[3]{(a+b)^4}}{\frac{1}{(a+b)^{-\frac{2}{3}}}}=\)
\(\sqrt[3]{a+b}*\sqrt[3]{(a+b)^4}*(a+b)^{-\frac{2}{3}}=\)
\(\sqrt[3]{(a+b)(a+b)^4}*\frac{1}{(a+b)^{\frac{2}{3}}}=\)
\(\sqrt[3]{(a+b)^5}*\frac{1}{\sqrt[3]{(a+b)^2}}=\)
\(\sqrt[3]{\frac{(a+b)^5}{(a+b)^2}=\)
\(\sqrt[3]{(a+b)^3}=a+b\)
Answer: E.
Hope it's clear.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Posts: 90
Bunuel
Thanks Bunuel, could you put an explanation of what you are doing for each step as you reduce the fractions?
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Answer = E
\(\frac{1}{\frac{1}{\sqrt[3]{a+b}}}*\frac{\sqrt[3]{(a+b)^4}}{\frac{1}{(a+b)^{-\frac{2}{3}}}}=\)
Get rid of the \(\sqrt{SQUARE ROOT}\) sign first
\(\frac{1}{\frac{1}{{(a+b)}^{\frac{1}{3}}}}*\frac{{(a+b)^{\frac{4}{3}}}}{\frac{1}{(a+b)^{-\frac{2}{3}}}}=\)
Normalize the denominator (Adjust power sign)
\(\frac{1}{{(a+b)}^{\frac{-1}{3}}}*\frac{{(a+b)^{\frac{4}{3}}}}{{(a+b)^{\frac{2}{3}}}=\)
Get rid of the denominator
\({{(a+b)}^{\frac{+1}{3}}} * (a+b)^{\frac{4}{3}} * (a+b)^{\frac{-2}{3}} =\)
Bases are the same; add the powers
\({{(a+b)}^{(\frac{+1}{3} - \frac{2}{3} + \frac{4}{3})} =\)
a+b
\(\frac{1}{\frac{1}{\sqrt[3]{a+b}}}*\frac{\sqrt[3]{(a+b)^4}}{\frac{1}{(a+b)^{-\frac{2}{3}}}}=\)
Get rid of the \(\sqrt{SQUARE ROOT}\) sign first
\(\frac{1}{\frac{1}{{(a+b)}^{\frac{1}{3}}}}*\frac{{(a+b)^{\frac{4}{3}}}}{\frac{1}{(a+b)^{-\frac{2}{3}}}}=\)
Normalize the denominator (Adjust power sign)
\(\frac{1}{{(a+b)}^{\frac{-1}{3}}}*\frac{{(a+b)^{\frac{4}{3}}}}{{(a+b)^{\frac{2}{3}}}=\)
Get rid of the denominator
\({{(a+b)}^{\frac{+1}{3}}} * (a+b)^{\frac{4}{3}} * (a+b)^{\frac{-2}{3}} =\)
Bases are the same; add the powers
\({{(a+b)}^{(\frac{+1}{3} - \frac{2}{3} + \frac{4}{3})} =\)
a+b
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
Moderator:
Announcements
Monday, Sep 14, 2026
11:30am NY / 3:30pm London / 9pm Mumbai
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.