Answer:
(a) 2.56197 x 10¹⁹
Explanation:
You want the sum of 2.53 x 10¹⁹ and 3.197 x 10¹⁷ written in scientific notation.
Addition
You can only add digits that have the same place value multiplier. When numbers are written in standard form, we make sure we're doing that by aligning the decimal points of the two numbers.
When numbers are in scientific notation, the decimal point shown is usually not the actual decimal point. Rather the exponent of 10 tells you where the decimal point is found.
For example, 10¹⁹ tells you the number's decimal point is 19 places to the right of where it is shown in 2.53×10¹⁹. Similarly, 3.197×10¹⁷ tells you the decimal point is 17 places to the right. If we want to align the decimal points, we need to have the power-of-ten multipliers have the same exponent:
2.53×10¹⁹ + 3.197×10¹⁷
= 2.53×10¹⁹ + 0.03197×10¹⁹
= 2.56197×10¹⁹
Technology
Any scientific or graphing calculator, and any spreadsheet can add these number more or less as they are written. Output can be formatted in scientific notation, too. The attachment shows a calculator used to sum the numbers.
Often a calculator or spreadsheet will use "E" in place of "×10^", as
2.56197E19 instead of 2.56197×10^19
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Additional comment
The use of E to signify the power of 10 comes from a period in computer history when typeset number formatting was unavailable, and character count was at a premium.