Question 209010
please help me solve this equation: 
<pre><font size = 4 color = "indigo"><b>
{{{(x^4y^(-5))/(x^(-8)z^2)^(-m)}}}  

Remove the parentheses on the bottom by multiplying
each inner exponent by the outer exponent {{{-m}}}

{{{(x^4y^(-5))/(x^((-8)(-m))z^((2)(-m)))}}}

{{{(x^4y^(-5))/(x^(8m)z^(-2m))}}}

Get rid of the negative exponents by 
1. Move them up or down across the fraction bar
2. Change the sign of the exponent to positive:

In this case we move the {{{y^(-5)}}} down to
the bottom as {{{y^5}}} and we move the {{{z^(-2m)}}}
up to the top as {{{z^(2m)}}} 

{{{(x^4z^(2m))/(x^(8m)y^5)}}}

Now subtract exponents of the x's

{{{(x^(4-8m)z^(2m))/(y^5)}}}

or if you prefer you can subtract
exponents the other way and get

{{{z^(2m)/(x^(8m-4)y^5)}}}

Either is correct since they are
equivalent.

=======================================

{{{((2x^(-5)y)/(y^(-8)*z^(-5)))^(-3)}}} 

Make sure every factor in both numerator
shows its exponent, whether it is a number 
or a letter, and even if it has exponent 1:

{{{((2^1x^(-5)y^1)/(y^(-8)*z^(-5)))^(-3)}}} 

Remove the parentheses by multiplying each
of the five inside exponents by the outside
exponent {{{-3}}}:

{{{(2^(1*(-3))x^(-5*(-3))y^(1*(-3)))/(y^(-8*(-3))*z^(-5*(-3)))}}}

{{{ (2^(-3)x^(15)y^(-3))/(y^24*z^15)  )}}}

Now we only have to move the factors with negative
exponents from top to bottom and change the signs
of the exponents to positive:

{{{ x^15/(2^3*y^3*y^24*z^15)  )}}}

Finally we write {{{2^3}}} as {{{8}}}
and add exponents of y:

{{{ x^15/(8*y^27*z^15)  )}}}

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