Final answer:
The smallest power of 10 that exceeds the number 45,086,925,186 is 1011, as we need to shift the decimal 11 places to the left to obtain a value between 1 and 10 in scientific notation.
Step-by-step explanation:
To find the smallest power of 10 that exceeds the number M=45,086,925,186, we need to determine how many times we can place the decimal point moving from right to left until we get a number between 1 and 10. In this case, we will be shifting the decimal 11 places, which means that the power of ten we are looking for is 1011. This is the smallest power of 10 that is still greater than M.
The number 45,086,925,186 written in scientific notation is approximately 4.5086925186 x 1010 (since the decimal has been moved 10 places to the left), but since we are looking for the smallest power of 10 that exceeds M, we must go to the next power, which is 10^11. Therefore, the correct answer is C) 10^11.