Final answer:
The expansion of 1000 to the power of 100 results in a number with 300 zeros following the initial digit 1, as 1000 can be represented as 10 to the power of 3, and that exponent is then multiplied by 100.
Step-by-step explanation:
When 1000100 is expanded out, the result is 1 followed by 300 zeros. This can be understood by recognizing that 1000100 is the same as 103 raised to the 100th power, as 1000 is 103. This means that we multiply the exponent 3 by 100, giving us 10300, which is a 1 followed by 300 zeros.
To clarify further, each time we raise 10 to a power, it increases the number of zeros. For instance, 102 equals 100, and 103 equals 1000, indicating a pattern where the exponent denotes the number of zeros following the digit 1. This pattern applies to 1000100 by converting 1000 into 103 and then applying the standard rules of exponents. Hence, we end up with 300 zeros after the digit 1.