Hello UG, I have asked multiple times for math help, and here I am asking again. I am confused on exponent laws. Can anyone answer this question, and explain how it works?

Simplify:
(x^2 y^-9)^1/3
*pretend theirs a line here*
(x^-2 y^6)^1/6

I am confused as to how to do this.
Quote by blair30

x y^-4

Id prefer if someone could back me up before I explain.

Just looked in the back of the book, that is correct.
First step: Get rid of the radical in the denominator.
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Quote by pepsi_lovr
Just looked in the back of the book, that is correct.

Tomosaurus feels this thread was an excuse not to do maths.
Keep up the good work!
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I go down on one knee and do that shit cello style

There was a special math thread made earlier today...you should've used it! Everyone would've thought you were way cool

Some people wait a lifetime, some simply accept...

...Some of us crash land, some of us eject...

...Some restore the blood flow, some just let it go and bleed...

...Some of us obsess, some move on to something new
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Math isn't cool, though.

Each to their own, but either way...the math thread is cooler than the deluge of maths threads we get every single week, it just gets annoying after a while

And makes me feel stupid
Some people wait a lifetime, some simply accept...

...Some of us crash land, some of us eject...

...Some restore the blood flow, some just let it go and bleed...

...Some of us obsess, some move on to something new
Quote by pepsi_lovr
Just looked in the back of the book, that is correct.

Woohoo!

Okay what I did was,

(x^2 y^-9)^1/3
/
(x^-2 y^6)^1/6

Multiply the powers inside the brackets with those outside.

ie, (numerator) x^2*^1/3 = x^2/3 and y^-9*^1/3 = y^-3

So on the top you have, x^2/3 y^-3

Do the same thing with the bottom and you should altogether get,

x^2/3 y^-3
/
x^-1/3 y^1

Now simplifying is easy.

x's will cancel to become x^1 (or just x)
y's will cancel to become y^-4