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Rational Exponents

Directions:  Fill in the boxes using the whole numbers 1 through 6 to make the largest (or smallest) possible number. Use each digit at most once.

Extension: How close to 1 can you get?



Which of the boxes should get the largest number? Which should get the smallest number?

There are 720 (6!) total possible arrangements of the numbers 1-6 in this equation… do you have to check them all?



The largest number is 140625 = (5/1)^(6) * 3^(4/2)
The smallest number is 0.0001076 = (1/5)^6 * 2^(3/4)
The closest to 1 is 1.01047 = (4/6)^1 * 2^(3/5)

Source:  Erick Lee

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