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

Question

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

BrentGMATPrepNow · Accepted Answer

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

Manonamission · Answer

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

Senthil1981 · Answer

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

AbdurRakib · Answer

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

Naeemeeda · Answer

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

ytsejam · Answer

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

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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