How can I simplify and solve this expression with negative exponents?

[Nelo]

Homework Statement

http://i51.tinypic.com/2zyfyaa.jpg

Question 3 l )

Homework Equations

The Attempt at a Solution

(6a^-2b^-3)^2
(__________) 1/6a^2 * 1/b^3 / 1/2a^2 * 1/b^1
(2a^2b^-1 )

I multiplied the top half together to give me 1/ 36a^4b^2

Multiplied the bottom half to give me 1/4a^4b^1 , Then took the reciprical of the bottom half and move it up and multiplied it with the top half.

Giving me a final of

:: 4a^4b^1
__________
36^a4b^5

However, when i fold this down it becomes 1/9 and the a's cancel and 4b is left over at the bottom.

The answer is a^8b^4 / 9

I know its complicated to read, just write it on paper and ull understand.

What did i do wrong?

 

[Nelo]

Or...

Look here.

http://www.purplemath.com/modules/simpexpo2.htm

Go down to Simplify the following expression: (–3x–1y2)2

Why is it 9y^4 / x^2 , and not 9x^2/y^4 , doesn't make sense? anyone?

 

[Nelo]

Or... f) (-3m^-3n^-1)^-3

Solving this one, I get -27m^9 / n^3

Why in the answer book is it m^9*m^3 /27 ?

Anyone...?

 

[eumyang]

You continue to write out your problems in a way that makes it hard to read. I think others would be less willing to help you because of this. Learn LaTeX, for goodness sake!

In any event, if I am reading your work correctly, this line:

I multiplied the top half together to give me 1/ 36a^4b^2

is wrong. It should be 1/ 36a^4b^6.

Anyway, your approach is rather confusing. It looks like you want to start by rewriting the negative exponents to positive ones. I wouldn't do that. Instead, divide the numerator by the denominator, subtracting exponents as you go:
\left(\frac{6a^{-2}b^{-3}}{2a^2 b^{-1}}\right)^{-2} = \left(3a^{-4}b^{-2} \right)^{-2}
Then "distribute" the -2 exponent that is outside the parentheses, and THEN rewrite any negative exponents that are remaining to positive ones.

 

[Nelo]

If i do it your way, then I get no fractions in my final answer. i just get 9a^8b^4, Sorry I don't know any other method except this recipricol one and its just not working.

I understand your step, but what step comes after How do i turn that into a fraction again

 

[eumyang]

Or... f) (-3m^-3n^-1)^-3

Solving this one, I get -27m^9 / n^3

Why in the answer book is it m^9*m^3 /27 ?

Anyone...?

You got it wrong because it looks like you think that
(-3)^{-3} = -27,
and it's not. It should be
(-3)^{-3} = -\frac{1}{27}.

Also, the answer book does not say that! Don't you see the typos? It should be
-\frac{m^9 n^3}{27}

 

[eumyang]

If i do it your way, then I get no fractions in my final answer. i just get 9a^8b^4

No, you should have gotten
\frac{1}{9}a^8 b^4 = \frac{a^8 b^4}{9}.
You're not applying the negative exponent to the coefficient correctly, it seems.

 

[Nelo]

Cept i do realize that it is 1/-27, and yes it is a typo, but my question remains the same. Why is that mn on top and the 27 on bottom .

When i work it out I get this...

= 1 1
____ * ____
-27m^6 n^3

Then I don't get why the m and n are on top and 27 is on bottom. Unless the n cross multipleis up to the left and the m^6 only cross multiplies to the other side... But that's probably not it.

 

[Nelo]

So.. you solved it like multiplication then did a recipriocol of the "9" for the final step..?

 

[gb7nash]

= 1 1
____ * ____
-27m^6 n^3

Type this instead:

[tex ]\frac{1}{-27m^6}*\frac{1}{n^3}[/tex ]

(without the space in the tex tags) You will save yourself and anyone who's reading your work lots of time.

 

[Nelo]

\frac{1}{-27m^6}*\frac{1}{n^3}

 

[eumyang]

Cept i do realize that it is 1/-27, and yes it is a typo, but my question remains the same. Why is that mn on top and the 27 on bottom .

When i work it out I get this...

= 1 1
____ * ____
-27m^6 n^3

Then I don't get why the m and n are on top and 27 is on bottom. Unless the n cross multipleis up to the left and the m^6 only cross multiplies to the other side... But that's probably not it.

But if you "distribute" the -3 exponent outside the parentheses first, you would get
\left(-3m^{-3}n^{-1}\right)^{-3} = (-3)^{-3}m^{9}n^{6}
It's much easier to simplify from this, as opposed to using the reciprocal method to start.

 

[Nelo]

Reopen my tinypic link, and look at 3k) . How do i solve that using your method? I simplified the top half then tried solving it and it failed.

I get to -10s^5 t^3
__________
4s^2 t^3

.

I get it this far. Now what am i supposed to do? ( I know I am not using your tex thing.. I don't know how and i don't really have time at the moment)

 

[Nelo]

Ok, well whatever I guess. Just answer me this then. If there is an expression that include both negetive and positive exponents, I keep the positive exponents where they are and recipricol the negitive ones yes?

 

[eumyang]

Reopen my tinypic link, and look at 3k) . How do i solve that using your method? I simplified the top half then tried solving it and it failed.

I get to -10s^5 t^3
__________
4s^2 t^3

This is wrong. It's supposed to be:
\frac{-10s^{-5}t^3}{4s^2 t^{-3}}
Now you can either subtract the exponents, or "flip" the variables that contain the negative exponents across the bar and make the exponents positive, like this:
\frac{-10 t^3 t^3}{4s^2 s^5}
I'll leave you to do the rest.

And if you must know, I didn't reply right away because it's morning here and I have to get ready for the day. The rest of us aren't chained to our computers 24 hours a day, you know. Now I have to run. Good luck.