(x^1/6y^1/3)^-18

- anonymous

(x^1/6y^1/3)^-18

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- anonymous

so I will do numerator and denominator separately

- anonymous

okay thank you :0]

- anonymous

numerator --(x^1)^-18=x^-18

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## More answers

- anonymous

now what is this numerator go to?

- anonymous

denominator -- (6y^1/3)^-18
=(6^-18)*(y^-6)

- anonymous

put them together
(x^-18)/(6^-18)(y^-6)

- anonymous

okay break this down a bit. for the numerator where did you get the x^1?

- anonymous

wasn't that in the question?

- anonymous

no its x^1/6

- anonymous

no its x^1/6

- anonymous

oh, I misread the question, sorry

- anonymous

its okay it was just hiding is all. haha

- anonymous

(x^(1/6) * y^(1/3))^-18
x^-3 y^-6

- anonymous

I just multiplied the exponents

- anonymous

theres no multiplication sign between x and y

- anonymous

when there is nothing, it is assumed that they are being multiplied

- anonymous

oh okay. so for the exponents do you just make the 3 qnd 6 equal to -18?

- anonymous

When you have one exponent on another like this
\[(a^x)^y\]
You would multiply the exponents
x*y

- anonymous

can be rewritten as a^(x*y)

- anonymous

xy^1/18?

- anonymous

so in your case
(x^(1/6) * y^(1/3))^-18

- anonymous

nvm i got it x^-3 and y^-6 right?

- anonymous

you are right

- anonymous

is that as simpilified as im going to get?

- anonymous

Yes

- anonymous

alrighty thank you for helping me :0]

- anonymous

btw do you know that negative exponent could be written as positive if you put in denominator

- anonymous

no i didn't but that might be important right?

- anonymous

yes say you have something like
x^-a
you can rewrite it as
1/x^a

- anonymous

1/ over the equation

- anonymous

okay yeah i saw that in a video i was recently watching okay thanks a lot!! that will help towards my test. i really really apperciate everything. :0]

- anonymous

also
remember this
x^a * y^b=z^(a+b)
x^a/y^b= z^(a-b)

- anonymous

special cases??

- anonymous

no it is always the case
Trying solving this
x^2 * y^4

- anonymous

z^6?

- anonymous

Yes

- anonymous

I forgot to say this but x and y must be same

- anonymous

sorry my computer is running slow. in the cases you just showed me is that what your talking about?

- anonymous

yes

- anonymous

yes

- anonymous

2^3 * 2^2 = 8 * 4= 32
or 2^(3+2) = 2^5= 32

- anonymous

Will you test have log

- anonymous

okay for a the problem im working on now (x^1/3 /y^-2/3)^9 do i divide first?

- anonymous

log? like on the calculator?

- anonymous

since you do not know if x and y are same don't devide anything

- anonymous

Just do what we did on last problem

- anonymous

i did i got x^3/y^-6 but my book says the answer os x^3y^6

- anonymous

-2/3 * 9

- anonymous

i got -6 and i did the same for 1/3 and got 3

- anonymous

Both you and the book are right

- anonymous

1/a^-x = a^x
1/a^x = a^-x

- anonymous

hmmm? but i have the x^3 on top how can you fit a 1 by itself?

- anonymous

This is what you got
x^3/y^-6
using
1/a^-x = a^x
1/a^x = a^-x
x^3 * 1/y^-6
x^3 * y^6

- anonymous

oh okay that makes more sense.

- anonymous

1 * x^3 just x^3

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