Question 459009
<pre>
{{{16^(-2a-1)=1/2}}}

Write 16 as 2&#8308;

{{{(2^4)^(-2a-1)=1/2}}}

Multiply the exponents on the left to
remove the parentheses:

{{{2^(-8a-4)=1/2}}}

Multiply both sides by 2

{{{2*2^(-8a-4)=2*expr(1/2)}}}

Add the understood 1 exponent of 2 on the left
to the other -8a-4 exponent of 2 on the left and 
get an exponent of -8a-4+1 or -8a-3

{{{2^(-8a-3)=1}}}

Replace the 1 on the right with 2<sup>0</sup>
(That may seem strange but it causes both sides
to be powers of the same base 2. You are 
accustomed to replacing 2<sup>0</sup> by 1 but
not to replacing 1 by 2<sup>0</sup>. So this
may be a first time with you).

{{{2^(-8a-3)=2^0}}}

Since the bases of exponents on each side of
the equation are the same positive number other
than 1, we may set the exponents equal:

So we set the exponents equal and drop the bases
of 2:

{{{-8a-3=0}}}

{{{-8a= 3}}}

{{{a=-3/8}}}

Edwin</pre>