Question 1148576
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There are many variations of how to simplify this expression.  The method you are asking about is one of them.  Here is how it might go....<br>
{{{16^log(4,8)}}}<br>
Rewriting each number as a power of 2....<br>
{{{(2^4)^(log(2^2,2^3))}}}<br>
Now in the exponent {{{(log(2^2,2^3))}}} you can use the "change of base formula"<br>
{{{log(b,a)= log(n,a)/log(n,b)}}}<br>
and choose n=2 as the base:<br>
{{{(log(2,2^3)/(log(2,2^2))) = 3/2}}}<br>
So now the expression is<br>
{{{(2^4)^(3/2) = 2^(4*(3/2)) = 2^6 = 64}}}<br>