Can somebody explain how to simplify this expression? Negative 2y to the negative 1 power, all inside parentheses, with a negative 2 exponent outside the parentheses.

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- anonymous

- schrodinger

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- amistre64

using math notation for staters

- amistre64

\[(-2y^{-1})^{-2}\]

- amistre64

this?

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## More answers

- amistre64

\[-2^{-2} y^2\]
\[-\frac{y^2}{4}\] maybe?

- radar

Is it still a minus (if it was inside the paren)?

- anonymous

Yes, you set it up right, amistre.

- radar

I suspect the answer may be \[y ^{2}\over 4\]

- radar

Maybe amisstrte64 will come back and verify his answer.

- anonymous

I think it is 4y^2

- anonymous

...because it looks like this is the expression...
(-2y^-1)^-2
Multiplying exponents
(-2y)^2
Expanding brackets
4y^2

- radar

I went this direction, but I do see your logic. I may have violated order of operations:\[(-2y ^{-1})^{-2}\] to:\[1\over (-2y ^{-1})^{2}\]then to:\[1\over 4 y ^{-2}\] finally\[y ^{2}\over 4\]

- anonymous

\[(-2y^{-1})^{-2}=(-2)^{-2}y^2=\frac{y^2}{(-2)^2}=\frac{y^2}{4}\]\]

- radar

Help me out here satellite73

- anonymous

if that was the problem to beginwith

- anonymous

we get \[\frac{y^2}{4}\] yes?

- anonymous

hello radar! here to celebrate amistre's 1000 medal

- radar

that is what i got, amistre got a -y^2/4

- anonymous

hope it is soon cause i got to run

- radar

before you run look at gianfranco solution above, what is wrong with that approach beside getting a different answer???

- anonymous

well if the question is as he wrote it, you have to raise (-2) to the power of -2, not the same as
\[-2^{-2}\]

- anonymous

you should get a 4 in the denominator

- anonymous

gianfraco was acting as if it was
\[((-2y)^{-1})^{-2}\]

- anonymous

but that is now how i read the problem. i read it as only the y being raised to the power of -1. if there were no parentheses that is what it means

- anonymous

i read it the way you did

- radar

I can see that that would make a difference.

- anonymous

of course. like the difference between \[(2\times 3)^2\] and \[2\times 3^2\]

- radar

Understand. Thanks for clearing up a few things.

- anonymous

O never mind everybody..I think I've figured it out.

- radar

I was hoping you would

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