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

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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If 27^p*3^2 = 3^4*9^8, what is the value of p?

Author Message
TAGS:

### Hide Tags

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

### Show Tags 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

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
WE: Engineering (Consulting)
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

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

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

### Show Tags

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

RELATED VIDEOS

PRACTICE QUESTION FOR REINFORCEMENT

_________________
Director  B
Status: I don't stop when I'm Tired,I stop when I'm done
Joined: 11 May 2014
Posts: 516
GPA: 2.81
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

### Show Tags

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.

Intern  B
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

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

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

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

Target Test Prep Representative V
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

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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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?  