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

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

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12 Aug 2016, 08:10
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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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Joined: 11 Jul 2016
Posts: 77
Re: If 27^p*3^2 = 3^4*9^8, what is the value of p?  [#permalink]

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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

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

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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

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

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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

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

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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.

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

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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

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

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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

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

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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

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