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# If m^(-1) = -1/3 then m^(-2) is equal to

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Manager
Joined: 08 Jun 2011
Posts: 77
If m^(-1) = -1/3 then m^(-2) is equal to  [#permalink]

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26 Jul 2011, 11:31
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Difficulty:

5% (low)

Question Stats:

88% (00:39) correct 12% (00:43) wrong based on 143 sessions

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If m^(-1) = -1/3 then m^(-2) is equal to

(A) -9
(B) -3
(C) -1/9
(D) 1/9
(E) 9

The answer is D and this is how OG12 explained it

m^-2 is (m^-1)^2 = m^-2. Therefore, we square all of -(1/3) which is = 1/9.

This is how I did it.

m^-1 = 1/m^1 Which in turn is 1/m.

This means that m^-2 = 1/m^2 .

So if 1/m = -(1/3) then 1/m^2 should be -(1/3^2) which is -(1/9). Why do I have to square the entire thing up? I am only squaring the bottom hence why would the negative sign go. Perhaps it's for the 1 and not for the 9?

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-1-1-3-then-m-2-is-equal-to-144451.html
Senior Manager
Joined: 28 Jun 2009
Posts: 344
Location: United States (MA)
Re: If m^(-1) = -1/3 then m^(-2) is equal to  [#permalink]

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26 Jul 2011, 11:52
1

Quote:
if 1/m = -(1/3) then 1/m^2 should be -(1/3^2) which is -(1/9).

You're right till
m^-2 = 1/m^2 and m^-1 = 1/m^1 = 1/m

given m^-1 = -(1/3) so, 1/m = -(1/3) solving this, m = -3
Now, m^-2 = 1/m^2 = 1/(-3)^2 = 1/9
Senior Manager
Joined: 03 Mar 2010
Posts: 323
Schools: Simon '16 (M$) Re: If m^(-1) = -1/3 then m^(-2) is equal to [#permalink] ### Show Tags 26 Jul 2011, 11:53 See it this way, $$1/m = -1/3$$ $$m= -3 ( not 3)$$ $$1/m = 1/-3$$ $$1/m^2 = 1/(-3)^2$$ $$1/m^2 = 1/9$$ $$m^-^2 = 1/9.$$ _________________ My dad once said to me: Son, nothing succeeds like success. Manager Joined: 08 Jun 2011 Posts: 77 Re: If m^(-1) = -1/3 then m^(-2) is equal to [#permalink] ### Show Tags 26 Jul 2011, 11:59 jamifahad wrote: See it this way, $$1/m = -1/3$$ $$m= -3 ( not 3)$$ $$1/m = 1/-3$$ $$1/m^2 = 1/(-3)^2$$ $$1/m^2 = 1/9$$ $$m^-^2 = 1/9.$$ So basically you assumed that m=-3 because there was a 1 in the top and 1 cannot possibly = -1 so the m had to have the negative sign, correct? Senior Manager Joined: 03 Mar 2010 Posts: 323 Schools: Simon '16 (M$)
Re: If m^(-1) = -1/3 then m^(-2) is equal to  [#permalink]

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26 Jul 2011, 12:06
Yes. But there is no assumption. It's a fact. It's math.
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My dad once said to me: Son, nothing succeeds like success.
Math Expert
Joined: 02 Sep 2009
Posts: 62380
Re: If m^(-1) = -1/3 then m^(-2) is equal to  [#permalink]

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16 May 2016, 01:31
If m^(-1) = -1/3 then m^(-2) is equal to

(A) -9
(B) -3
(C) -1/9
(D) 1/9
(E) 9

The answer is D and this is how OG12 explained it

m^-2 is (m^-1)^2 = m^-2. Therefore, we square all of -(1/3) which is = 1/9.

This is how I did it.

m^-1 = 1/m^1 Which in turn is 1/m.

This means that m^-2 = 1/m^2 .

So if 1/m = -(1/3) then 1/m^2 should be -(1/3^2) which is -(1/9). Why do I have to square the entire thing up? I am only squaring the bottom hence why would the negative sign go. Perhaps it's for the 1 and not for the 9?

$$m^{-1} = -\frac{1}{3}$$ --> $$\frac{1}{m}=-\frac{1}{3}$$ --> $$m=-3$$ --> $$m^{-2}=\frac{1}{m^2}=\frac{1}{9}$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-m-1-1-3-then-m-2-is-equal-to-144451.html
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Re: If m^(-1) = -1/3 then m^(-2) is equal to   [#permalink] 16 May 2016, 01:31
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