Answer
$\frac{1}{10^4}$
Work Step by Step
$(\frac{10^6}{10^8})^2\longrightarrow$ to raise a power to a power, multiply the exponents
$=\frac{10^{12}}{10^{16}}^\longrightarrow$ to divide powers subtract the exponents
$=10^{12-16}$
$=10^{-4}\longrightarrow$ express the result using a positive exponent
$=\frac{1}{10^4}$