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so I will do numerator and denominator separately

okay thank you :0]

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

now what is this numerator go to?

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

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

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

wasn't that in the question?

no its x^1/6

no its x^1/6

oh, I misread the question, sorry

its okay it was just hiding is all. haha

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

I just multiplied the exponents

theres no multiplication sign between x and y

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

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

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

can be rewritten as a^(x*y)

xy^1/18?

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

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

you are right

is that as simpilified as im going to get?

Yes

alrighty thank you for helping me :0]

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

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

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

1/ over the equation

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

special cases??

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

z^6?

Yes

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

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

yes

yes

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

Will you test have log

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

log? like on the calculator?

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

Just do what we did on last problem

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

-2/3 * 9

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

Both you and the book are right

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

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

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

oh okay that makes more sense.

1 * x^3 just x^3