After clarification we see the respective diameters are
[tex]A = 2.3 \times 10^{-a}[/tex]
[tex]B = 2.3 \times 10^{-b}[/tex]
We're asked about the ratio
[tex]A:B = 2.3 \times 10^{-a} : 2.3 \times 10^{-b} = 10^{-a} : 10^{-b} = 10^b : 10^a = 10^{b-a} : 1[/tex]
Now we can go through the choices.
A. If a = 4 and b = 6, then cell a is 100 times greater than cell b.
[tex] A:B=10^{6-4}:1 = 100:1[/tex]
It would be more proper to say the diameter of cell A is 100 times the diameter of cell B, but yes, this is TRUE.
B. If a = 4 and b = 6, then cell b is 100 times greater than cell a.
FALSE. 10 to the minus 4 is 100 times bigger than 10 to the minus 6, so a is bigger.
C. If a = 4 and b = 6, then cell a is 2 times greater than cell b.
FALSE. We already calculated its 100 times bigger.
D. If a = 4 and b = 6, then cell b is 2 times greater than cell a.
FALSE.
