Reviewing some math basics before I start college.
I'm unsure of a few things, so please check my work as I go. Thank you.
First question:
2c. Simplify the following expression. Write your answer without negative exponents.

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- Jamierox4ev3r

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- Jamierox4ev3r

Give me some time to type out the expression, thanks.

- Jamierox4ev3r

\[\left( \frac{ 3x ^{\frac{ 3 }{ 2 }}y ^{3} }{ x ^{2} y ^{-\frac{ 1 }{ 2 }}} \right)^{-2}\]

- Jamierox4ev3r

oh my goodness that was a heck of an expression to get out.
So far, what I've done is this:
\[\left( \frac{ x ^{2}y ^{-\frac{ 1 }{ 2 }} }{ 3x ^{\frac{ 3 }{ 2 }} y ^{3}} \right)^{2}\]
basically, I got ride of the negative 2 exponent by flipping the fraction around. If this was an incorrect thing to do, someone let me know now. My recollection of algebra rules is a bit foggy

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## More answers

- Jamierox4ev3r

any idea? @Nnesha

- Nnesha

wait lol :P

- Jamierox4ev3r

alright :P thanks

- Nnesha

alright back

- Nnesha

sorry abt that i need to buy a new laptop >.<
i'm just gonna use draw tool
|dw:1440364115001:dw|
but i'm sure we will get the same answer :=) yes

- Jamierox4ev3r

lol nice xD \(\LaTeX\) is complicated stuffs

- Nnesha

that's the same thing as this
\[\left( \frac{ x ^{2}y ^{-\frac{ 1 }{ 2 }} }{ 3x ^{\frac{ 3 }{ 2 }} y ^{3}} \right)^{2}\]
so yes your first step is right
wanna try next step :=)

- Nnesha

this is the 3rd time i was about to use equation tool
but my laptop turned off so i'm like ugghh

- Jamierox4ev3r

Sure. Here is what I think I should do next
Distribute the 2 exponent. So I would get this:
\[ \frac{ x ^{4} y ^{-1}}{ 9x ^{3}y ^{6} }\\]

- Jamierox4ev3r

oh man xD let me try that again
\(\Large\frac{x^{4} y^{-1}}{9x^{3}y^{6}}\)

- Nnesha

yes that's right ! doing great so far!

- Jamierox4ev3r

There we go! and :oo I did correct things! Yay me cx

- Jamierox4ev3r

Kinda confused from there, but if I recall correctly, then I would simplify as follows:
\(\Large\frac{xy^{-7}}{9}\)

- Jamierox4ev3r

would that be a correct way of simplifying?

- Nnesha

perfect!

- Nnesha

one more step!

- Jamierox4ev3r

wao! alright I wasn't even sure if that was correct XD
So last of all, I assume that since we don't want any negative exponents for the final simplified form, we would put the y in the denominator in order to eliminate the negative exponent. It would look like this:
\(\Large\frac{x}{9y^{7}}\)

- Jamierox4ev3r

and I'm assuming that I have arrived at the final answer

- Jamierox4ev3r

...I think

- Nnesha

YAY!!

- Nnesha

that's it!

- Jamierox4ev3r

It's right? :o

- Jamierox4ev3r

YES!

- Jamierox4ev3r

oh my gosh, I didn't think I remembered any of this algebra, it's been almost 3 long years since I've done this stuff. Thank you so much <33

- Nnesha

eh i didn't do anything :/
you posted this question to tell me how SMART you are :(

- Nnesha

hahh jk you gonna get A+ good luck wth ur college stuff!

- Jamierox4ev3r

Thank you so so much XD I didn't know if I was heading in the right direction to be honest, in my textbook, there's no answer key for any of the review. So I just tried things and crossed my fingers lol. Thanks for helping me make sure that I was doing the right thing.

- Nnesha

my pleasure! <3

- triciaal

all the best with college. be confident relax and ask for help when you really need it .

- Jamierox4ev3r

@triciaal thank you so much! I really appreciate it. I'm pretty nervous to begin college honestly, but reviewing early concepts is a good way to prep. for the higher math courses that I'm going to be taking in the extremely near future. To be precise, in two days! Thank you for you advice, I will make sure I ask for help whenever I need it and do my best to always remain confident in my abilities.

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