Question 94608
my worksheet says to simplify this problem, could you please help me? thank you 

{{{ (4a^3b^(-4))^3/(20a^(-3)b^3)}}}
<pre><font size = 4><b>
Indicate the exponent of 4 on top as 1, so
every factor inside the parentheses will
have its exponent showing:

{{{ (4^1a^3b^(-4))^3/(20a^(-3)b^3)}}}

To remove the parentheses on top, multiply
each exponent inside the parentheses by
the outer exponent, 3:

{{{ (4^(1*3)a^(3*3)b^(-4*3))/(20a^(-3)b^3)}}}

{{{ (4^3a^9b^(-12))/(20a^(-3)b^3)}}}

To get rid of the negative exponents, 

1. Move the {{{b^(-12)}}} from top to bottom
   and change the {{{-12}}} exponent from
   negative to positive, so that we will have
   {{{b^12}}} as a factor on the bottom.

2. Move the {{{a^(-3)}}} from bottom to top
   and change the {{{-3}}} exponent from
   negative to positive, so that we will have
   {{{a^3}}} as a factor on the top.

{{{ (4^3a^9a^3)/(20b^3b^12)}}}

To multiply the exponential factors in the 
top, add their exponents {{{9+3}}} = {{{12}}}

and to multiply the exponential factors in 
the bottom, add their exponents {{{3+12}}} = {{{15}}}

{{{ (4^3a^12)/(20b^15)}}}

Now replace the {{{4^3}}} with {{{64}}}

{{{ (64a^12)/(20b^15)}}}

Finally divide the 64 and the 20 both by 4

{{{ (16a^12)/(5b^15)}}}

Edwin</pre>