Question 124362
Please help: 
Type using only positive exponents: 
{{{(36x^(-4)y^2z^0)/(5x^2y^(-3)z^(-2))}}} 
<pre><font size = 4 color = "indigo">><b>
Immediately when we see a factor which has a zero
exponent, we replace the whole base and exponent
by the number 1.  So  

{{{(36x^(-4)y^2z^0)/(5x^2y^(-3)z^(-2))}}}

becomes

{{{(36x^(-4)y^2(1))/(5x^2y^(-3)z^(-2))}}}

or just

{{{(36x^(-4)y^2)/(5x^2y^(-3)z^(-2))}}}

Next use this rule about fractions which have 
numerator and/or denominator factors with
negative exponents:

If a factor on top has a negative exponent,
then bring it to the bottom and change its
exponent from negative to positive:

and the "vice-versa" of it:

If a factor on the bottom has a negative 
exponent, then bring it to the top and change 
its exponent from negative to positive:

{{{(36x^(-4)y^2)/(5x^2y^(-3)z^(-2))}}}

So we bring the {{{x^(-4)}}} from the top
to the bottom but change the sign of its
exponent to positive, so we erase the {{{x^(-4)}}}
in the top and put {{{x^4}}} in the bottom. I'll
put it on the bottom right: 

{{{(36y^2)/(5x^2y^(-3)z^(-2)x^4)}}} 

Next we bring the {{{y^(-3)}}} from the bottom
to the top but change the sign of its
exponent to positive, so we erase the {{{y^(-3)}}}
on the bottom and put {{{y^3}}} in the top. I'll
put it on the top right: 

{{{(36y^2y^3)/(5x^2z^(-2)x^4)}}}

Next we bring the {{{z^(-2)}}} from the bottom
to the top but change the sign of its
exponent to positive, so we erase the {{{z^(-2)}}}
on the bottom and put {{{z^2}}} in the top. I'll
put it on the top right also:

{{{(36y^2y^3z^2)/(5x^2x^4)}}}

Now we have all the exponents positive, so all
we need do is simplify by adding exponents:
We replace {{{y^2y^3}}} in the top by {{{y^5}}}

{{{(36y^5z^2)/(5x^2x^4)}}}

Next we replace {{{x^2x^4}}} in the bottom by {{{x^6}}}

{{{(36y^5z^2)/(5x^6)}}}

That's the final answer.

Now you need to type that in using the standard keyboard
symbols.  BTW you had your original expression typed wrong.

You have this:

36x^-4 y^2 z^0 / 5x^2 y^-3 z^-2

But that means the same as this:

{{{36x^(-4)y^2((z^0)/5)x^2y^(-3)z^(-2)}}}

not this

{{{(36x^(-4)y^2z^0)/(5x^2y^(-3)z^(-2))}}} 

Your mistake in typing was the failure to place
parentheses around any numerator or denominator 
when it is necessary to tell the computer where 
the numerator or denominator starts and where it 
stops.  

To type your final answer, 

{{{(36y^5z^2)/(5x^6)}}}

using standard keyboard characters, this is what
you type:

(36y^5z^2)/(5x^6)

Notice that the parenthese around the numerator and
denominator tell the computer or reader where they
starts and where they end.

If you were to type this instead:

36y^5z^2/5x^6

it would be wrong, for if you fail to
indicate where a numerator or denominator
starts and stops it is automatically assumed
that the numerator and denominator contain
as few factors as possible.  So if you left
off the parentheses it would be understood
to be: 

{{{36y^5(z^2/5)x^6}}}

which would be wrong since that is different 
from this:

{{{(36y^5z^2)/(5x^6)}}}

Edwin</pre></font></b>