It is currently 20 Feb 2018, 07:43

### 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

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If 2^(8x) = 640000, then what is the value of 2^(2x−2)?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43828
If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

22 Feb 2017, 02:46
2
KUDOS
Expert's post
8
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

62% (01:50) correct 38% (02:14) wrong based on 77 sessions

### HideShow timer Statistics

If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 19 Apr 2016
Posts: 275
Location: India
GMAT 1: 570 Q48 V22
GMAT 2: 640 Q49 V28
GPA: 3.5
WE: Web Development (Computer Software)
If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

22 Feb 2017, 03:01
5
KUDOS
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

$$2^{(8x)} = 640000 = 2^6*10^4$$
$$2^{(2x)} = 2^{6/4}*10^{4/4}$$
$$2^{(2x)} = 2^{3/2}*10$$
$$2^{(2x)} = 2\sqrt{2}*10 = 20\sqrt{2}$$

$$2^{(2x-2)} = 20\sqrt{2}/4 = 5\sqrt{2}$$

Hence Option A is correct
Hit Kudos if you liked it

Last edited by 0akshay0 on 22 Feb 2017, 21:29, edited 1 time in total.
Manager
Joined: 31 Jan 2017
Posts: 58
Location: India
GMAT 1: 680 Q49 V34
GPA: 4
WE: Project Management (Energy and Utilities)
Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

22 Feb 2017, 05:59
In the step

2^(2x)=20√2 is OK

Now
2^(2x−2)=2^(2X) / 2^2 = 20√2 / 4 = 5√2
_________________

__________________________________
Kindly press "+1 Kudos" if the post helped

Intern
Joined: 26 Dec 2016
Posts: 27
Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

12 Jan 2018, 17:41
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

what was your approach to this Bunuel because I'm not quite following the posted solution. Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 43828
Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

12 Jan 2018, 23:20
1
KUDOS
Expert's post
rnz wrote:
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

what was your approach to this Bunuel because I'm not quite following the posted solution. Thanks!

Step 1:

$$2^{(8x)} = 640000$$;

$$(2^{2x})^4 = 2^{10}*5^4$$;

$$2^{2x} = 2^{(\frac{5}{2})}*5$$;

$$2^{2x} = \sqrt{2^5}*5$$;

$$2^{2x} = 20\sqrt{2}$$.

Step 2:

$$2^{(2x−2)}=\frac{2^{(2x)}}{2^2}$$.

Step 2:

Substitute $$2^{2x} = 20\sqrt{2}$$ into $$\frac{2^{(2x)}}{2^2}$$.:

$$\frac{20\sqrt{2}}{2^2}=5\sqrt{2}$$.

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43828
Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

12 Jan 2018, 23:22
SVP
Joined: 11 Sep 2015
Posts: 2051
Re: If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

13 Jan 2018, 06:01
Expert's post
Top Contributor
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

Another approach:

Given: 2^(8x) = 640000
Raise both sides to the power 1/2 (aka take square root of both sides) to get: [2^(8x)]^(1/2) = 640000^(1/2)
Simplify to get: 2^(4x) = 800
Raise both sides to the power 1/2 (again) to get: [2^(4x)]^(1/2) = 800^(1/2)
Simplify: 2^2x = √800
Simplify: 2^2x = 20√2
Divide both sides by 2² (aka 4) to get: (2^2x)/2² = (20√2)/4
Simplify both sides to get: 2^(2x - 2) = 5√2

RELATED VIDEOS

_________________

Brent Hanneson – Founder of gmatprepnow.com

Math Expert
Joined: 02 Aug 2009
Posts: 5657
If 2^(8x) = 640000, then what is the value of 2^(2x−2)? [#permalink]

### Show Tags

13 Jan 2018, 06:22
Bunuel wrote:
If $$2^{(8x)} = 640000$$, then what is the value of $$2^{(2x−2)}$$?

A. 5√2
B. 10
C. 10√2
D. 80√2
E. 160

Another approach, although most of these approaches is solving the equation..

Let $$2^{(2x−2)}=y$$, so $$y^4=2^{(2x−2)*4}=2^{8x-8}=\frac{2^{8x}}{2^8}=\frac{640000}{2^6*2^2}=\frac{10000}{2^2}$$
so $$y^4=\frac{10000}{2^2}=\frac{10^4}{2^2}....y=\frac{10}{\sqrt{2}}=5\sqrt{2}$$

A
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

BANGALORE/-

If 2^(8x) = 640000, then what is the value of 2^(2x−2)?   [#permalink] 13 Jan 2018, 06:22
Display posts from previous: Sort by