180 Days of Ideas for Discussion in Math Class. (as of 9July2014, we're in overtime!)

I want to say 8 but that seems too obvious to me. Have I missed something?

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I believe the only allowable possibilities are(2^2)^6 = (2^3)^4 = (2^4)^3 = (2^6)^2Since the only prime factor of 2^12 is 2, the same must be true for b, and the only ways to write 12 as an ordered product of integers greater than 1 is(2)(6) = (3)(4) = (4)(3) = (6)(2)In other words, the possibilities are:1. a = 2^2 = 4 and b = 62. a = 2^3 = 8 and b = 43. a = 2^4 = 16 and b = 34. a = 2^6 = 64 and b = 2

I want to say 8 but that seems too obvious to me. Have I missed something?

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ReplyDeleteI believe the only allowable possibilities are

ReplyDelete(2^2)^6 = (2^3)^4 = (2^4)^3 = (2^6)^2

Since the only prime factor of 2^12 is 2, the same must be true for b, and the only ways to write 12 as an ordered product of integers greater than 1 is

(2)(6) = (3)(4) = (4)(3) = (6)(2)

In other words, the possibilities are:

1. a = 2^2 = 4 and b = 6

2. a = 2^3 = 8 and b = 4

3. a = 2^4 = 16 and b = 3

4. a = 2^6 = 64 and b = 2