If 3^m3^m3^m = 9^n, then m/n =

Question

If  3^m3^m3^m = 9^n , then  \frac{m}{n} =

A. 1/3 
B. 2/3 
C. 1 
D. 3/2 
E. 3

dheeraj7890 · Answer

3^m3^m3^m = 9^n
3^(m+m+m)=(3^2)^n
3^3m=3^2n
3m=2n
m/n = 2/3

rajat198 · Answer

3^m*3^m*3^m= 9^n
3^(m+m+m)= 3^2n
3^3m=3^2n

=> 3m=2n => m/n=2/3

answer is b...

PareshGmat · Answer

3^m 3^m 3^m = 9^n

(3*3*3)^{m} = 3^{2n}

3^{3m} = 3^{2n}

Bases are same; equating powers

3m = 2n

\frac{m}{n} = \frac{2}{3}

Answer = B

pacifist85 · Answer

I also soved it, but a bit differently. Thank you for reminding me of this much easier and logical way!

What I did was to test powers of 3 that would lead to 9.

So, we have 3 raised to the same power 3 times and 9 raised to another power one time: 3^m3^m3^m = 9^n

What I did was test 3 raised to the power of 2 like this:
3^2*3^2*3^2 = 9*9*9 = 9^3. This means that m=2 and n=3. So, m/n=2/3.

It wouldn't be that hard ot back solve using the answer choices as well.

TeamGMATIFY · Answer

The easiest way to solve such questions is to bring the numbers in the same base. 
Always try to bring the base to the lowest number possible, in this case: 3

3^m*3^m*3^m = 9^n
3^(3m) = 3^2n
Since the bases are same, we can equate the powers.

3m = 2n
Therefore m/n = 2/3
Option B

GMATasian · Answer

---

Hi sorry for a stupid question. The question asked for m/n right?

why is the answer 2/3 and NOT 3/2? the answer we got is 2m=2n

Bunuel · Answer

If  3^m3^m3^m = 9^n , then  \frac{m}{n} =

A. 1/3 
B. 2/3 
C. 1 
D. 3/2 
E. 3

3^m3^m3^m = 9^n ;

3^{(m+m+m)} = 3^{2n}

3^{3m} = 3^{2n}

3m = 2n ;

Divide by n:  3*\frac{m}{n}=2 .

Divide by 3:  \frac{m}{n}=\frac{2}{3} .

Answer: B.

AkshdeepS · Answer

3^m3^m3^m = 9^n

3^3m = 3^2n

As bases are same , we can equate powers,

3m = 2n

\frac{m}{n}= \frac{2}{3}

(B)

hoang221 · Answer

3^m3^m3^m = 9^n => 3^{3m} = 3^{2n} => 3m = 2n => \frac{m}{n} = \frac{2}{3}  => (B)

JeffTargetTestPrep · Answer

When bases are the same, we add the exponents. Thus, 3^m*3^m*3^m = 3^3m. Simplifying the equation, we have:

3^3m = 9^n

3^3m = 3^2n

3m = 2n

m/n = 2/3

Answer: B

EgmatQuantExpert · Answer

Solution:

Given:

• 3^m* 3^m * 3^m = 9^n

Working out:

We need to find the value of  m/n

Per our conceptual knowledge, we know that if the numbers are in multiplicative form. We can add their powers, provided their bases are same.

Here, applying the same concept, we get:

•  3^{m+m+m} = 9^n

• Or,  3^{3m} = 9^n

• Or,  3^{3m} = (3^2)^n

• Or,  3^{3m} = 3^{2n}

Since the bases are same, we can equate the exponents.

Following the above process, we get:

•  3m = 2n

• Or,  m/n = 2/3

Answer: Option B

hemantbafna · Answer

3^m3^m3^m = 9^n
(3)^3m=3^2n
As the bases are same we can equate the powers.

3m=2n
m/m=2/3
 B

Abhishek009 · Answer

3^m3^m3^m = 9^n

Or,  3^{3m} = 3^{2n}

So,  \frac{3m}{2n} = 1

Or,  \frac{m}{n} = \frac{2}{3} , Answer must be (B)

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