simplify 3...4 sqrt(x)sqrt(y) (sqrt(xy)^3 / x^-2y^3(sqrt(x))

[humakhan]

3....................4
sqrt(x)sqrt(y) ( sqrt(xy)^3
-----------------------------------
x^-2 y^3 (sqrt(x) )^3 y^-3

HUH
help

do you understand how i did this?
if not than i can attach the pic here

 

[galactus]

Sorry, humakhan, it's hard to follow. Since you post on here frequently, you might want to learn some LaTex.

Like this, for instance.

\(\displaystyle \frac{a+b}{a-b}\)

Click on quote at the upper right corner of this post to see the code I used to make it display like that.

 

[stapel]

do you understand how i did this?

What did you do? If what you posted is your answer, then what was the question? If what you posted was the question, what is your answer?

Please reply using standard formatting (or LaTeX), clearly stating the exercise and its instructions, and showing all the steps in your work.

Thank you.

Eliz.

 

[Denis]

WHAT the heck does that "3............4" mean? :shock:

 

[galactus]

That's what had me stymied. :?

 

[soroban]

Re: simplify 3...4 sqrt(x)sqrt(y) (sqrt(xy)^3 / x^-2y^3(sqrt

Hello, humakhan!

Are you trying to indicate different roots?
I'll take a guess at what you meant . . .

\(\displaystyle \L\frac{\sqrt[3]{x}\,\cdot\,\sqrt{y}\,\cdot\,\left(\sqrt[4]{xy}\right)^3} {x^{-2}\,\cdot\,y^3\,\cdot\,\left(\sqrt{x}\right)^3\,\cdot\,y^{-3}}\)

First of all, the \(\displaystyle y^3\) and the \(\displaystyle y^{-3}\) in the denominator will cancel.

We have: \(\displaystyle \L\:\frac{x^{\frac{1}{3}}\,\cdot\,y^{\frac{1}{2}}\,\cdot\,\left[\left(xy\right)^{\frac{1}{4}}\right]^3}{x^{-2}\,\cdot\,\left(x^{\frac{1}{2}}\right)^3} \;=\;\frac{x^{\frac{1}{3}}\,\cdot\,y^{\frac{1}{2}}\,\cdot\,(xy)^{\frac{3}{4}}}{x^{-2}\,\cdot\,x^{\frac{3}{2}}} \;=\;\frac{x^{\frac{1}{3}}\,\cdot\,y^{\frac{1}{2}}\,\cdot\,x^{\frac{3}{4}}\,\cdot\,y^{\frac{3}{4}} }{x^{-\frac{1}{2}} }\)

\(\displaystyle \L\;=\;\left(x^{\frac{1}{3}}\,\cdot\,x^{\frac{3}{4}}\,\cdot\,x^{\frac{1}{2}}\right)\,\cdot\,\left(y^{\frac{1}{2}}\,\cdot\,y^{\frac{3}{4}}\right) \;= \;x^{\frac{19}{12}}\,\cdot\,y^{\frac{5}{4}}\)

 

[humakhan]

Re: simplify 3...4 sqrt(x)sqrt(y) (sqrt(xy)^3 / x^-2y^3(sqrt

Hello, humakhan!

Are you trying to indicate different roots?
I'll take a guess at what you meant . . .

\(\displaystyle \L\frac{\sqrt[3]{x}\,\cdot\,\sqrt{y}\,\cdot\,\left(\sqrt[4]{xy}\right)^3} {x^{-2}\,\cdot\,y^3\,\cdot\,\left(\sqrt{x}\right)^3\,\cdot\,y^{-3}}\)

First of all, the \(\displaystyle y^3\) and the \(\displaystyle y^{-3}\) in the denominator will cancel.

We have: \(\displaystyle \L\:\frac{x^{\frac{1}{3}}\,\cdot\,y^{\frac{1}{2}}\,\cdot\,\left[\left(xy\right)^{\frac{1}{4}}\right]^3}{x^{-2}\,\cdot\,\left(x^{\frac{1}{2}}\right)^3} \;=\;\frac{x^{\frac{1}{3}}\,\cdot\,y^{\frac{1}{2}}\,\cdot\,(xy)^{\frac{3}{4}}}{x^{-2}\,\cdot\,x^{\frac{3}{2}}} \;=\;\frac{x^{\frac{1}{3}}\,\cdot\,y^{\frac{1}{2}}\,\cdot\,x^{\frac{3}{4}}\,\cdot\,y^{\frac{3}{4}} }{x^{-\frac{1}{2}} }\)

\(\displaystyle \L\;=\;\left(x^{\frac{1}{3}}\,\cdot\,x^{\frac{3}{4}}\,\cdot\,x^{\frac{1}{2}}\right)\,\cdot\,\left(y^{\frac{1}{2}}\,\cdot\,y^{\frac{3}{4}}\right) \;= \;x^{\frac{19}{12}}\,\cdot\,y^{\frac{5}{4}}\)

oh god thats extactly it
You got what i was saying when i scaned the picture and was about to post it as a attachment. = )
thank you so much for your help.
by the way how do you write that problem in that form.......
i have been here since last year and i still dont know how to write that way
how do ?

 

[humakhan]

Hello, humakhan!

Are you trying to indicate different roots?
I'll take a guess at what you meant . . .

\(\displaystyle \L\frac{\sqrt[3]{x}\,\cdot\,\sqrt{y}\,\cdot\,\left(\sqrt[4]{xy}\right)^3} {x^{-2}\,\cdot\,y^3\,\cdot\,\left(\sqrt{x}\right)^3\,\cdot\,y^{-3}}\)

ok you know where you have y^-3 i made a mistake it had ot be y^-2
sorry

ok now what do i have to do the same ways but different steps