Final answer:
To subtract exponentials, ensure numbers have the same power of 10 and subtract the digit terms. Similar steps apply to addition where you add the digit terms after converting to the same power of 10. Adjustments may be necessary to keep the digit term between 1 and 10.
Step-by-step explanation:
When working with the power (exponent) of 10, it is important to understand how to perform operations like addition and subtraction. To subtract exponentials, you need to make sure the numbers are expressed with the same power of 10. First, convert all numbers to the same power of 10, and then subtract the digit terms. For instance, if you have 3 x 105 - 2 x 105, you would simply subtract the digit terms getting 1 x 105. If necessary, you can then adjust the resulting number to ensure the digit term is between 1 and 10.
For addition of exponentials, the process is similar. Convert the numbers to the same power of 10, and then add the digit terms together. If we add 3 x 104 + 7 x 104, the result is 10 x 104. If necessary, adjust the exponential term to maintain a digit term between 1 and 10, resulting in 1 x 105.
Remember, the exponent's value indicates how many places the decimal point is shifted, making it an efficient way to notate very large or very small numbers. For example, 6,000 can be expressed as 6 x 103 as the decimal point is shifted 3 places to the right.