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What is the value of a^(-2)*b^(-3)?

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What is the value of a^(-2)*b^(-3)? [#permalink] New post 11 Nov 2010, 09:02
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What is the value of a^(-2)*b^(-3)?

(1) a^(-3)*b^(-2)=36^(-1).
(2) ab^(-1)=6^(-1)
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Last edited by monirjewel on 10 Jul 2013, 20:08, edited 2 times in total.
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Re: Value of a^-2 b^-3 [#permalink] New post 11 Nov 2010, 10:07
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What is the value of a^-2*b^-3?

Note that we are not told that a and b are integers.

a^{-2}*b^{-3}=\frac{1}{a^2b^3}=? So, basically we need to find the value of a^2b^3.


(1) a^{-3}*b^{-2}=36^{-1} --> a^3b^2=36. Not sufficient.
(2) ab^{-1}=6^{-1} --> \frac{b}{a}=6. Not sufficient.

(1)+(2) Multiply (1) by (2): a^3b^2*\frac{b}{a}=a^2b^3=36*6. Sufficient.

Answer: C.
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Re: Value of a^-2 b^-3 [#permalink] New post 11 Nov 2010, 11:51
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Statement 1 alone is clearly insufficient since we have an additional ab^-1 present.
Statement 2 alone is also not adequate to calculate a^-2*b^-3

Multiplying both statements above- (a^-3*b^-2) *(a*b^-1) = a^-2*b^-3

which is 6/36 = 1/6,

Answer:- C
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Re: Value of a^-2 b^-3 [#permalink] New post 12 Nov 2010, 10:10
Good question. +1.
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Re: Value of a^-2 b^-3 [#permalink] New post 22 Feb 2012, 01:39
I am a bit confused on (1)

Here is the way I thought:
(a^-3)(b^-2)=(36^-1)
(1/a^3)(1/b^2)=1/36
(a^3)(b^2)=36
(a^3)(b^2)=(3^2)(2^2)
(a^3)(b^2)=(1^3)(6^2)
a= 1 ; b = 6

How using fractions would make this reasoning wrong?
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Re: Value of a^-2 b^-3 [#permalink] New post 22 Feb 2012, 01:49
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wizard wrote:
I am a bit confused on (1)

Here is the way I thought:
(a^-3)(b^-2)=(36^-1)
(1/a^3)(1/b^2)=1/36
(a^3)(b^2)=36
(a^3)(b^2)=(3^2)(2^2)
(a^3)(b^2)=(1^3)(6^2)
a= 1 ; b = 6

How using fractions would make this reasoning wrong?


You are missing one point: we are not told that a and b are integers, hence from a^3*b^2=36 you can not say for sure that a=1 and b=6. Because for ANY a there will exits some b which will satisfy a^3*b^2=36 (and vise-versa). For example if a=2 then b^3=9 and b=\sqrt[3]{9}.

Similar question to practice: if-3-a-4-b-c-what-is-the-value-of-b-1-5-a-25-2-c-106047.html

Hope it helps.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink] New post 22 Feb 2012, 01:53
Thanks for the example. It is clear.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink] New post 15 Aug 2012, 23:32
Answer is C .

From 1: 1/a^3 *1/b^2= 1/36 Not sufficient
From 2 : 1/ab =1/6 means a, b can be :2,3 ; 3,2 ;6,1;1,6 . not sufficient

Combining both statements only a=1 and b=6 fulfills the statement 1 so answer is C

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Re: Value of a^-2 b^-3 [#permalink] New post 13 Sep 2012, 06:53
Bunuel wrote:
What is the value of a^-2*b^-3?

Note that we are not told that a and b are integers.

a^{-2}*b^{-3}=\frac{1}{a^2b^3}=? So, basically we need to find the value of a^2b^3.


(1) a^{-3}*b^{-2}=36^{-1} --> a^3b^2=36. Not sufficient.
(2) ab^{-1}=6 --> \frac{b}{a}=\frac{1}{6}. Not sufficient.

(1)+(2) Multiply (1) by (2): a^3b^2*\frac{b}{a}=a^2b^3=36*\frac{1}{6}. Sufficient.

Answer: C.


Hi all, I would like to add to the explanation given by Bunuel.
(1)as explained by bunuel a^3b^2=36 - Insufficient ----> Why?
Because we can be sure that a=1 but we b can be either +6 or -6
(2) b = 6a----Insufficient because this is just a ratio & nothing is mentioned about their values.

Hope it helps.
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Re: Value of a^-2 b^-3 [#permalink] New post 13 Sep 2012, 06:59
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fameatop wrote:
Bunuel wrote:
What is the value of a^-2*b^-3?

Note that we are not told that a and b are integers.

a^{-2}*b^{-3}=\frac{1}{a^2b^3}=? So, basically we need to find the value of a^2b^3.


(1) a^{-3}*b^{-2}=36^{-1} --> a^3b^2=36. Not sufficient.
(2) ab^{-1}=6 --> \frac{b}{a}=\frac{1}{6}. Not sufficient.

(1)+(2) Multiply (1) by (2): a^3b^2*\frac{b}{a}=a^2b^3=36*\frac{1}{6}. Sufficient.

Answer: C.


Hi all, I would like to add to the explanation given by Bunuel.
(1)as explained by bunuel a^3b^2=36 - Insufficient ----> Why?
Because we can be sure that a=1 but we b can be either +6 or -6
(2) b = 6a----Insufficient because this is just a ratio & nothing is mentioned about their values.

Hope it helps.


Let me correct you: we cannot be sure that a=1 from (1). Since we are not told that a and b are integers, then a could, for example be 2 and b could be -\frac{3}{\sqrt{2}} or \frac{3}{\sqrt{2}}.

Hope it's clear.

P.S. This post might also help: what-is-the-value-of-a-2-b-104673.html#p1047996
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Re: Value of a^-2 b^-3 [#permalink] New post 10 Jul 2013, 07:01
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Bunuel wrote:
What is the value of a^-2*b^-3?

Note that we are not told that a and b are integers.

a^{-2}*b^{-3}=\frac{1}{a^2b^3}=? So, basically we need to find the value of a^2b^3.


(1) a^{-3}*b^{-2}=36^{-1} --> a^3b^2=36. Not sufficient.
(2) ab^{-1}=6 --> \frac{b}{a}=\frac{1}{6}. Not sufficient.

(1)+(2) Multiply (1) by (2): a^3b^2*\frac{b}{a}=a^2b^3=36*\frac{1}{6}. Sufficient.

Answer: C.


small typo here :
statement 2 says : ab^{-1}=6^{-1} and not ab^{-1}=6 so we have \frac{a}{b} = \frac{1}{6}
so a^2b^3= a^3 *b^2 * \frac{b}{a} = 36 *6 = 216 and not \frac{36}{6}

Hope it helps
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Re: Value of a^-2 b^-3 [#permalink] New post 10 Jul 2013, 07:04
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stne wrote:
Bunuel wrote:
What is the value of a^-2*b^-3?

Note that we are not told that a and b are integers.

a^{-2}*b^{-3}=\frac{1}{a^2b^3}=? So, basically we need to find the value of a^2b^3.


(1) a^{-3}*b^{-2}=36^{-1} --> a^3b^2=36. Not sufficient.
(2) ab^{-1}=6 --> \frac{b}{a}=\frac{1}{6}. Not sufficient.

(1)+(2) Multiply (1) by (2): a^3b^2*\frac{b}{a}=a^2b^3=36*\frac{1}{6}. Sufficient.

Answer: C.


small typo here :
statement 2 says : ab^{-1}=6^{-1} and not ab^{-1}=6 so we have \frac{a}{b} = \frac{1}{6}
so a^2b^3= a^3 *b^2 * \frac{b}{a} = 36 *6 = 216 and not \frac{36}{6}

Hope it helps


Yes, exponent was missing in the second statement. Edited. Thank you.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink] New post 13 Jul 2013, 15:11
Bunuel,

Even if we were told a&b are postive integers does knowing a^3*b^2=constant ever gaurentee knowing the value of a^2*a^3??

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Re: What is the value of a^(-2)*b^(-3)? [#permalink] New post 13 Jul 2013, 22:41
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alphabeta1234 wrote:
Bunuel,

Even if we were told a&b are postive integers does knowing a^3*b^2=constant ever gaurentee knowing the value of a^2*a^3??

Posted from my mobile device Image


Well, if we were told that a and b are positive integers, then from a^3b^2=36 it follows that a=1 and b=6.
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Re: What is the value of a^(-2)*b^(-3)?   [#permalink] 13 Jul 2013, 22:41
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