Final answer:
To compute the expression 9.6*10^141 + (6.4*10^140)/(3.2*10^16), we first perform the division resulting in 2*10^124 and then add this to 9.6*10^141. Given the significant difference in exponents, the overall sum is unaffected by the smaller term, resulting in a final answer of 9.6*10^141.
Step-by-step explanation:
The student is asking to evaluate the expression 9.6 \( \times \) 10^141 + (6.4 \( \times \) 10^140) / (3.2 \( \times \) 10^16) and express the answer in standard form, which is a procedure in mathematics involving scientific notation and operations on powers of ten.
First, let's handle the division part of the expression:
6.4 \( \times \) 10^140 / 3.2 \( \times \) 10^16 = 2 \( \times \) 10^124.
This is because 6.4 divided by 3.2 gives us 2, and the exponents are subtracted when dividing numbers in scientific notation (140 - 16 = 124).
Now we add this result to the first part of the expression:
9.6 \( \times \) 10^141 + 2 \( \times \) 10^124 = 9.6 \( \times \) 10^141 + 0.00000000000002 \( \times \) 10^141 (by aligning the powers of ten).
However, since the second term is significantly smaller than the first term, it does not affect the sum in this case, and thus the final answer is simply 9.6 \( \times \) 10^141.
Remember, when adding numbers in scientific notation, we can only directly add the coefficients if the exponents are the same. Here, the difference in magnitude between the exponents is so great that the smaller term does not affect the overall sum.