Question

What is the result of the operation (6.21248 x 10^-7) (3.48 x 10^21) expressed in exponential notation?

a) 2.16 x 10^15
b) 2.16 x 10^14
c) 2.16 x 10^22
d) 2.16 x 10^23

Answer 1

The result of the operation (6.21248 x 10^-7) (3.48 x 10^21) is 2.16 x 10^15 in scientific notation, which corresponds to answer choice (a).

Step-by-step explanation:

To find the result of the operation (6.21248 x 10^-7) (3.48 x 10^21), we can use the properties of exponents in multiplication. The rule is to multiply the base numbers and add the exponents when the base is 10. This operation looks like the following when we apply the rule:

• First, multiply the base numbers: 6.21248 × 3.48 = 21.6198224.
• Next, add the exponents of 10: (-7) + 21 = 14.
• Now, combine these results to get 21.6198224 x 10^14.
• In order to express the answer in scientific notation, we'll need to adjust 21.6198224 so that it is between 1 and 10. Moving the decimal point one place to the left gives us 2.16198224, and we need to increase our exponent by 1 to compensate, resulting in 2.16198224 x 10^15.

Finally, rounding to two decimal places as per the options provided, we have 2.16 x 10^15, which is answer choice (a).