Polynomial division

This is a problem that came in a set of problems where the answers are set up like this: a X^b Y^c Z^d sometimes the problem might not have all components and thats fine.

an example of a problem would be: (2^1 Z^5)^1
...............................................-----------
.................................................(X^-3 )
The answer would be: 2 Z^5 X^3

Now the problem I need help on is: (Y^-1/8 Z^-3/7)
..............................................------------------
.................................................. ..(5^2 Z^9 )

As i'm sure you know, the carrots ^ mean exponents. And i don't know how to set up fartions so those dashed lines mean that it's set up as a fraction. So sorry for all these inconvienences!

Thank you all very much if you read this and try to help, This is my first post and im excited to see if anyone reads and helps. I'm in a math class online that has to be completed by august 5 and im very far behind due to my lack of math skill but hopefully this site helps! THANK YOU AGAIN!

You would have observed that the X^-3 inthe denominator became X^+3 in the numerator. Similarly Y^-1/8 in the numerator will become Y^+1/8 in the denominator. Similarly for Z

Again,Law of Indices states that A^m x A^n = A^(m+n).Do that for Z.

How did the negative become positive? Just picture the x^-3 being multiplied with X^+3. By the above law that would give youX^0 which = 1.However,you cannot simply multiply the denominator and not the numerator.So you multiply the numerator also with X^+3.

Come back with a post if you get stuck somewhere.

So you are in exponents.

Basics:
>>>a^b * a^c = a^(b+c)
>>>a^b / a^c = a^(b-c)
>>>(a^b)^c = a^(b*c)

About negative exponents:
If the exponent is negative, "it is in the wrong place".
If the negative exponent (truly, a number with a negative exponent) is in the numerator, that means the number should be in the denominator (and the exponent becomes positive).
Likewise, if the negative exponent is in the denominator, that means the number should be in the numerator.

>>>a^0 = 1

So,
1 / a^b = a^0 / a^b = a^(0-b) = a^(-b)
Or, a^(-b) = 1 / a^b

1 / a^(-b) = 1* a^b = a^b
Or,
1 / a^(-b) = 1 / [a^(-b)] = 1 / [ 1 / a^b] = 1 * [a^b /1] = a^b

--------------------------------------

(Y^-1/8 Z^-3/7)
------------------
(5^2 Z^9 )

Rewriting that in one line only,
[y^(-1/8) z^(-3/7)] / [5^2 z^9]

We first make all exponents be positive, so we put the two terms with negative exponents from the numerator into the denominator,
= 1 / [5^2 y^(1/8) z^(3/7) z^9]

= 1 / [25 y^(1/8) z^(3/7 +9)]

= 1 / [25 y^(1/8) z^((3+63)/7)]

= 1 / [25 y^(1/8) z^(66/7)] ----answer.

If you want no fraction,
= 5^(-2) y^(-1/8) z^(-66/7) ----answer.