If a = 3^3*2^9, b = 3^6 *7^3, c = 2^6*5^3, which of the following is

Question

If  a=3^3*2^9 ,  b= 3^6 *7^3 ,  c = 2^6*5^3 , which of the following is true?

A.  c>b>a

B.  b>a>c

C.  a>c>b

D.  b>c>a

E.  c>a>b

JeffTargetTestPrep · Accepted Answer

a = 3^3 × 2^9
b = 3^6 × 7^3
c = 2^6 × 5^3

If we raise each of the above positive numbers to the power of 1/3, the order of the resulting numbers will correspond to the order of the original numbers.

a^(1/3) = (3^3 × 2^9)^(1/3) = 3 × 2^3 = 24
b^(1/3) = (3^6 × 7^3)^(1/3) = 3^2 × 7 = 63
c^(1/3) = (2^6 × 5^3)^(1/3) = 2^2 × 5 = 20

Since b^(1/3) > a^(1/3) > c^(1/3), we have:

b > a > c

Answer: B

Papai21 · Answer

Given 
a = 3^3 * 2^9 = 27 * 2^9 = (27 * 2^3) * 2^6 = (27 * 8) * 2^6 = 216 * 2^6
b = 3^6 * 7^3 = 343 * 3^6
c = 2^6 * 5^3 = 125 * 2^6

Now comparing b to c we see that b = 343 * 3^6 and c = 125 * 2^6. We see that term 343 in b is greater than 125 in c and also term 3^6 is greater than term 2^6. So it is clear that b>c

Similarly comparing a to b we see that a = 216 * 2^6 and b = 343 * 3^6. From this also we clearly see that term 343 in b is greater than 216 in a and term 3^6 in b is also greater than 2^6 in a. So clearly b>a

Thus combining we have, b>a>c
Hence answer choice B

BhavyaJha · Answer

Hi  karishma

Please guide how to equalize base or exponent in this case.

ThatDudeKnows · Answer

Compare these two things:

3^6 *7^3  vs.  2^6*5^3

They both have something-to-the-power-of-six times something-to-the-power-of-three.
The thing on the left has a larger base value for each.
The thing on the left is obviously larger. Cool, b>c. A, C, and E are out.

We don't need to compare a to b since both remaining answer choices have b>a.

All that's left is to find whether a>c or c>a.

3^3*2^9  vs.  5^3*2^6

Get rid of  2^6

3^3*2^3  vs.  5^3

27*8  vs.  125

The first one is clearly larger. a>c. D is out.

Answer choice B.

Harshani · Answer

Here is my solution
IT is clear that B is the biggest. This can help us elimiate all answer choices except B & D which gives us a 50/50

elslyknight · Answer

Encountered this in LBS' free mock and their explanation is a good concept in Exponent comparative questions - Reduce the expressions to either the same power or same base.

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abhikc3004 · Answer

This was very helpful, thank you so much!

If a = 3^32^9, b = 3^6 7^3, c = 2^6*5^3, which of the following is

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