Final answer:
To solve the given expressions, use the properties of exponents and standard arithmetic operations, carefully converting between scientific and standard notation as required.
Step-by-step explanation:
The student has asked to solve expressions and express the answers in both scientific and standard notation. When solving these types of problems, it's important to use the rules of exponents and maintain precision until the final answer is reached. Next, the scientific notation should be adjusted so the coefficient is a number between 1 and 10 multiplied by 10 raised to an integer power.
Examples:
3×107 in standard notation is 30,000,000.
8.4×1010 in standard notation is 84,000,000,000.
In scientific notation, if we multiply 4.6 × 10-5 by 2.09 × 103, we use the properties of exponents to get (4.6×2.09)×(10-5 × 103) = 9.594 × 10-2.
To express a number in standard notation from scientific notation, you expand the power of ten. For example, 6.022 × 1023 in standard notation is a 6 followed by 23 zeros.