I am so lost right now, can someone please help? This is properties of exponents 10th grade level. will post it below -->

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I am so lost right now, can someone please help? This is properties of exponents 10th grade level. will post it below -->

Mathematics
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\[(\frac{ 2yx^2*-y^-1z^0 }{ x^-3*2y^0z^-1 })~~ ^3\]
I got -y^3 x^15 z^3 , but i tried to used an online slover to check and it got something different so now im confused
Is this the problem? \[\Large \left(\frac{2yx^2*-y^{-1}z^0}{x^{-3}*2y^0z^{-1}}\right)^3\]

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Yes
I'm not getting the same answer you got
I just got all mixed up, i know how to solve these but i saw this and my mind went blank
notice how we have a 'y' term without an exponent up top that's the same as y^1 what is y^1 times y^(-1) equal to?
y^0 or y^-1 I don't know if i should add them or multiply
add \[\Large y^1*y^{-1} = y^{1+(-1)} = y^0\]
anything to the zeroth power is 1, so y^0 = 1
ok so that elliminates y
yes so y is nowhere in the final answer
the same would be said about z since z^0 = 1 up top but there is a z^(-1) down below that changes things
sorry if i have any late replies, i am making sure i right this down
that's fine
I also forgot about the y^0 down below, that also turns into 1 but I'm sure you see that by now
yes, i got that part :)
ok great
ok right now i have x^6 / x^-9 z^-3 ? am i close
good. I would have taken another route: simplify the inner stuff before multiplying the exponents. Either way works though.
now simplify \[\Large \frac{x^6}{x^{-9}z^{-3}}\]
x^15 z^3 ?
correct
oh one last thing though. There's a negative in there. When you cube -1 you get -1 so the result is negative
the online solver somehow got -x^6 z^3 / x^-9 , is my simplified answer still correct?
well the solver didn't fully simplify
the x^6 over x^(-9) simplifies to x^15
i used cymath.com (because it shows me steps) and ohhhh okay
so the final answer that I'd go for is \[\Large -x^{15}z^3\] since that's the most simplified in my view
okay :) so i was almost right in the beginning i just included "y" which wasn't supposed to exist lol thank you!
you're welcome, you did really good on it

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