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

This is a thing that made me look twice at it: 2^6 * 2^6 = 2^11 + 2^11. — Kate Nowak (@k8nowak) January 21, 2014

Nice.3^8 * 3^8 = 3^15 + 3^15 + 3^15

and how about 3^3 * 3^3 = 3^5 + 3^5 + 3^5 ?

n^x * n^x = n(n^(2x-1)) looks like a generalization of the above, with appropriate restrictions on n & x. So for n = 2, and x = 6, we get 2^6 * 2^6 = 2(n^(2*2-1) = n^11 + n^11and for n = 3 and x = 8 we get 3^8 * 3^8 = 2(3^(15) = 3^15 + 3^15and for n= 3 and x = 3 we get 3^3 * 3^3 = 3(3^5) = 3^5 + 3^5 + 3^15This allows us to generate infinite examples of this sort of thing. e.g., 5^6 * 5^6 = 5(5^11) = 5^11+5^11+5^11+5^11+5^11You can see why this works if you factor the right side as 5^11(1 + 1 + 1 + 1 + 1) =5^11 * 5 = 5^`12

Good stuff!!

Nice.

ReplyDelete3^8 * 3^8 = 3^15 + 3^15 + 3^15

and how about 3^3 * 3^3 = 3^5 + 3^5 + 3^5 ?

ReplyDeleten^x * n^x = n(n^(2x-1)) looks like a generalization of the above, with appropriate restrictions on n & x.

ReplyDeleteSo for n = 2, and x = 6, we get 2^6 * 2^6 = 2(n^(2*2-1) = n^11 + n^11

and for n = 3 and x = 8 we get 3^8 * 3^8 = 2(3^(15) = 3^15 + 3^15

and for n= 3 and x = 3 we get 3^3 * 3^3 = 3(3^5) = 3^5 + 3^5 + 3^15

This allows us to generate infinite examples of this sort of thing.

e.g., 5^6 * 5^6 = 5(5^11) = 5^11+5^11+5^11+5^11+5^11

You can see why this works if you factor the right side as 5^11(1 + 1 + 1 + 1 + 1) =

5^11 * 5 = 5^`12

Good stuff!!

Delete