Question 326523
if {{{(4a)^3}}}{{{""=""}}}{{{(2a)^2}}} 
What is a?
<pre><b>
{{{(4a)^3}}}{{{""=""}}}{{{(2a)^2}}}

Make sure every factor inside each set of parentheses
shows its exponent, even when it is 1:

{{{(4^1a^1)^3}}}{{{""=""}}}{{{(2^1a^1)^2}}}

Now remove the parentheses by multiplying each exponent
within the parentheses by the exponent outside the
parentheses:

{{{4^(1*3)a^(1*3)}}}{{{""=""}}}{{{2^(1*2)a^(1*2)}}}

{{{4^3a^3}}}{{{""=""}}}{{{2^2a^2}}}

Write {{{4^3}}} as {{{64}}} and {{{2^2}}} as {{{4}}}

{{{64a^3}}}{{{""=""}}}{{{4a^2}}}

Get 0 on the right side:

{{{64a^3}}}{{{""-""}}}{{{4a^2}}}{{{""=""}}}{{{"0"}}}

Factor {{{4a^2}}} out of the left side:

{{{4a^2}}}{{{"("}}}{{{16a}}}{{{""-""}}}{{{1}}}{{{")"}}}{{{""=""}}}{{{"0"}}}

Use the zero-factor property to set each factor equal to 0:

{{{matrix(3,5,

   4a^2=0, "", "", "", 16a-1=0,
    a^2=0, "", "", "",  16a=1,
      a=0, "", "", "",   a=1/16)}}} 

So there are two solutions.

Edwin</pre>