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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]  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) $$a*b^{(-1)}=6^{(-1)}$$
[Reveal] Spoiler: OA

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Last edited by Bunuel on 30 Jan 2015, 05:04, edited 3 times in total.
Edited the question.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  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.

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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  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,

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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  12 Nov 2010, 10:10
Good question. +1.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  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: What is the value of a^(-2)*b^(-3)? [#permalink]  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 a point there: we are NOT told that $$a$$ and $$b$$ are integers, hence from $$a^3*b^2=36$$ you cannot say for sure that $$a=1$$ and $$b=6$$. Because for ANY $$a$$ there will exist 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]  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]  15 Aug 2012, 23:32

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: What is the value of a^(-2)*b^(-3)? [#permalink]  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.

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: What is the value of a^(-2)*b^(-3)? [#permalink]  13 Sep 2012, 06:59
Expert's post
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.

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: What is the value of a^(-2)*b^(-3)? [#permalink]  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.

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: What is the value of a^(-2)*b^(-3)? [#permalink]  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.

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]  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??

Posted from my mobile device
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  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

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]  22 Jan 2015, 08:29
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  29 Jan 2015, 17:12
Hi Bunuel - can you explain why ab^(-1)=6^(-1) yields b/a = 6?
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  29 Jan 2015, 19:47
It would make it much clearer if you edited the original question to indicate for statement two "a * b^(-1)". I got confused and thought the whole term ab was taken to the negative first power.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  30 Jan 2015, 05:04
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Derkus wrote:
It would make it much clearer if you edited the original question to indicate for statement two "a * b^(-1)". I got confused and thought the whole term ab was taken to the negative first power.

In this case it would be (ab)^(-1), not ab^(-1). Still edited.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  30 Jan 2015, 05:06
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cg0588 wrote:
Hi Bunuel - can you explain why ab^(-1)=6^(-1) yields b/a = 6?

$$a*b^{(-1)}=6^{(-1)}$$;

$$a*\frac{1}{b}=\frac{1}{6}$$;

$$\frac{a}{b}=\frac{1}{6}$$;

$$\frac{b}{a}=6$$.

Hope it's clear.
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Re: What is the value of a^(-2)*b^(-3)? [#permalink]  30 Jan 2015, 13:56
Bunuel - thanks for the crystal clear explanation!
Re: What is the value of a^(-2)*b^(-3)?   [#permalink] 30 Jan 2015, 13:56
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