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

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

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

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA
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Re: If m^(-1) = -1/3 then m^(-2) is equal to [#permalink]

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26 Jul 2011, 11:52
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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
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Re: If m^(-1) = -1/3 then m^(-2) is equal to [#permalink]

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26 Jul 2011, 11:53
See it this way,
$$1/m = -1/3$$
$$m= -3 ( not 3)$$
$$1/m = 1/-3$$
$$1/m^2 = 1/(-3)^2$$
$$1/m^2 = 1/9$$
$$m^-^2 = 1/9.$$
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Re: If m^(-1) = -1/3 then m^(-2) is equal to [#permalink]

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26 Jul 2011, 11:59
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?
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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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Re: If m^(-1) = -1/3 then m^(-2) is equal to [#permalink]

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15 May 2016, 23:28
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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

[Reveal] Spoiler:
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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