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

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Bunuel
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If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  12 Aug 2016, 09:10
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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
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BrentGMATPrepNow
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If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  Updated on: 28 May 2020, 09:29
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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: B

Originally posted by BrentGMATPrepNow on 12 Aug 2016, 11:33.
Last edited by BrentGMATPrepNow on 28 May 2020, 09:29, edited 1 time in total.
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Manonamission
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  12 Aug 2016, 09:17
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
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  12 Aug 2016, 09:18
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
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  13 Aug 2016, 06:45
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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
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  19 Aug 2016, 06:13
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
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ytsejam
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  19 Aug 2016, 23:12
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
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ScottTargetTestPrep
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  09 Feb 2020, 05:22
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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
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink] New post  21 Feb 2021, 11:45
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Re: If 27^p*3^2 = 3^4*9^8, what is the value of p? [#permalink]
21 Feb 2021, 11:45
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