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b. 2,000
To determine the difference in magnitude between the two numbers, we divide 4 x 10^4 by 2 x 10^2:
(4 x 10^4) / (2 x 10^2) = (4/2) x 10^(4-2) = 2 x 10^2
So, 4 x 10^4 is 2,000 times larger than 2 x 10^2.