GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 28 Mar 2020, 10:58

### 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
Your Progress

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

# If 27^p*3^2 = 3^4*9^8, what is the value of p?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 62287
If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

12 Aug 2016, 08:10
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:06) correct 11% (01:35) wrong based on 142 sessions

### HideShow timer Statistics

If $$27^p*3^2 = 3^4*9^8$$, what is the value of p?

A. 3
B. 6
C. 8
D. 15
E. 16

_________________
Manager
Joined: 11 Jul 2016
Posts: 77
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

12 Aug 2016, 08:17
Bunuel wrote:
If $$27^p*3^2 = 3^4*9^8$$, what is the value of p?

A. 3
B. 6
C. 8
D. 15
E. 16

27^p .3^2 = 3^4 .9^8
=> 3^3p . 3^2 = 3^4. 3^2.8
=> 3^(3p+ 2) = 3^(4+16)
=> 3p + 2 = 20
=> p = 6 option B

Senior Manager
Joined: 23 Apr 2015
Posts: 271
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

12 Aug 2016, 08:18
Converting $$27^p*3^2 = 3^4*9^8$$ to prime factors form, $$3^{3*p} * 3^2 = 3^4 * 3^{2*8}$$
Just equate the powers and solve for p = 6

Answer is B 6
GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4540
Location: Canada
GMAT 1: 770 Q49 V46
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

12 Aug 2016, 10:33
1
Top Contributor
Bunuel wrote:
If $$27^p*3^2 = 3^4*9^8$$, what is the value of p?

A. 3
B. 6
C. 8
D. 15
E. 16

For equations with a variable in the exponent, it's useful to rewrite both sides of the equation with the SAME BASES.
Here, it appears we can rewrite 27 and 9 sides as powers of 3.
We'll replace 27 with 3^3, and we'll replace 9 with 3^2

Given: (27^p)(3^2) = (3^4)(9^8)
Replace to get: [(3^3)^p](3^2) = (3^4)[(3^2)^8]
Apply power of a power law to get: (3^3p)(3^2) = (3^4)(3^16)
Apply product law to get: 3^(3p +2) = 3^20
Since the bases are equal, we can conclude that 3p + 2 = 20
Solve to get p = 6

Answer:

RELATED VIDEOS

PRACTICE QUESTION FOR REINFORCEMENT

_________________
Test confidently with gmatprepnow.com
Director
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 516
Location: Bangladesh
Concentration: Finance, Leadership
GPA: 2.81
WE: Business Development (Real Estate)
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

13 Aug 2016, 05:45
1
Top Contributor
Bunuel wrote:
If $$27^p*3^2 = 3^4*9^8$$, what is the value of p?

A. 3
B. 6
C. 8
D. 15
E. 16

$$27^p*3^2 = 3^4*9^8$$
or,$$27^p=3^2*9^8$$
or,$$27^p=3^2*3^{16}$$
or,$$27^p=3^{18}$$
or,$$27^p=27^6$$

So,p=6.

Correct Answer B
Intern
Joined: 06 Nov 2014
Posts: 4
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

19 Aug 2016, 05:13
If 27^p∗3^2=3^4* 9^8, what is the value of p?

=(3^3)^p *3^2 =3^4*(3^2)^8
=3^3p*3^2 = 3^4*3^16
= 3^(3p+2)=3^(4+16)
= 3p+2=4+16
3p=4+16-2
p=18/3
p=6

Answers is B
Intern
Joined: 29 Mar 2015
Posts: 10
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

19 Aug 2016, 22:12
The trick is to make the terms on both sides with a common base and equate the powers. 3^(3p+2)=3^20
p=6

Answer is B
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9874
Location: United States (CA)
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

09 Feb 2020, 04:22
Bunuel wrote:
If $$27^p*3^2 = 3^4*9^8$$, what is the value of p?

A. 3
B. 6
C. 8
D. 15
E. 16

Simplifying, we have:

3^(3p) * 3^2 = 3^4 * 3^16

3^(3p + 2) = 3^20

The bases are equal, so we can equate the exponents and solve for p.

3p + 2 = 20

3p = 18

p = 6

Answer: B
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?   [#permalink] 09 Feb 2020, 04:22
Display posts from previous: Sort by

# If 27^p*3^2 = 3^4*9^8, what is the value of p?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne