Question 750612
<pre>
See how you like this way where we get rid of parentheses first.
I'm going to take more steps than necessary because you can do 
several of these steps all in one step:

{{{expr((3m^(-5)n)^4/(9m^2n^(-2)) )*(4mn^3)^2}}}

1. We make sure every factor shows its 1 exponent if it doesn't already 
have another exponent.  Like this:

{{{expr((3^1m^(-5)n^1)^4/(9^1m^2n^(-2)) )*(-4^1m^1n^3)^2}}}

2. When you have a fraction multiplied by a non-fraction, make the
non-fraction into a fraction by putting a 1 under it:

{{{expr((3^1m^(-5)n^1)^4/(9^1m^2n^(-2)) )*expr((-4^1m^1n^3)^2/1)}}}

3. Next remove the parentheses by distributing every exponent
that is inside the parentheses times the exponent just outside the
parentheses. The -4 will be squared so we can just ignore the negative
dign: 

{{{expr( (3^4m^(-20)n^4)/(9^1m^2n^(-2)) )*expr((4^2m^2n^6)/1)}}}

4. There are only two negative exponents. The rule is: Move the
factors with negative exponents on the bottom to the top, and on
the top to the bottom, and change the sign of the exponent to
positive.  So we move m<sup>-20</sup> to the bottom as m<sup>20</sup> and we move n<sup>-2</sup> to the top as n<sup>2</sup>.

{{{expr( (3^4n^2n^4)/(9^1m^2m^20) )*expr((4^2m^2n^6)/1)}}}

5. Let's just have one big fraction:

{{{ (3^4n^2n^4*4^2m^2n^6)/(9^1m^2m^20) }}}   

6. Let's add the exponents of like letters in order to multiply:

{{{ (3^4n^12*4^2m^2)/(9^1m^22) }}}

7. Let's subtract the exponents larger minus smaller
and place the result where the larger exponent was
The m<sup>22</sup> is on the bottom and the m<sup>2</sup> is on the
top. So we subtract exponents 22-2 and get 20 and write m<sup>20</sup> on
the bottom because the larger exponent was on the bottom.

{{{ (3^4n^12*4^2)/(9^1m^20) }}}

8.  Write the 9<sup>1</sup> as 9 and then as 3<sup>2</sup>

{{{ (3^4n^12*4^2)/(3^2m^20) }}}

9. Subtract the exponents of 3 and get 3<sup>2</sup> on the top
because the largere exponent was on top. 

{{{ (3^2n^12*4^2)/(m^20) }}}

10. Write 3<sup>2</sup> as 9 and  4<sup>2</sup> as 16

{{{ (9n^12*16)/(m^20) }}} 

11. Multiply the 9 by the 16 and get 144

{{{ (144n^12)/(m^20) }}}

Edwin</pre>