GRE Prep 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.
If 27^p*3^2 = 3^4*9^8, what is the value of p?
[#permalink]
21 Feb 2021, 10:45
21 Feb 2021, 10:45
Expert Reply
00:00
Question Stats:
91% (00:47) correct
8% (00:59) wrong based on 24 sessions
Hide Show 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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 3
B. 6
C. 8
D. 15
E. 16
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?
[#permalink]
21 Feb 2021, 10:53
21 Feb 2021, 10:53
1
Solution:
We can start by converting all the base values to 3 to get,
\(3^3^p*3^2 = 3^4*3^2^*^8\)
As these are in the exponential form with same base, we can add the power.
\(3^3^p^+^2=3^4^+^1^6\)
3p+2=20
3p=18
p=6
IMO B
Hope this helps!
We can start by converting all the base values to 3 to get,
\(3^3^p*3^2 = 3^4*3^2^*^8\)
As these are in the exponential form with same base, we can add the power.
\(3^3^p^+^2=3^4^+^1^6\)
3p+2=20
3p=18
p=6
IMO B
Hope this helps!
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?
[#permalink]
21 Feb 2021, 12:09
21 Feb 2021, 12:09
Carcass 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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 3
B. 6
C. 8
D. 15
E. 16
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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: B
