To multiply (2.36 x 10^8) by (108.4 x 10^5), we can multiply the numerical parts and add the exponents of 10:
(2.36 x 10^8) * (108.4 x 10^5) = (2.36 * 108.4) x (10^8 * 10^5) = 255.664 x 10^(8+5) = 255.664 x 10^13
The final answer, written in scientific notation, is 2.55664 x 10^14.