exponents Exponents Linear, Quadratic, and Exponential Models*

(16x^2)^3/4 = 1024x^11/4



OK OK OK I think I’ve got where 1024 comes from but what is going on with that 11?

Update: I think banderson2 nails it in the comments. “It comes from the power of 2. 2 = 8/4 so 8/4 + 3/4 is 11/4.”

7 replies on “(16x^2)^3/4 = 1024x^11/4”

The layout of the expression is bad. The 3/4 is too big, and should be at the same level as the 2.

I agree that the exponent comes from the equivalence of the mixed number 2 3/4 with the fraction 11/4. However, I’m not clear on what operations or what (overgeneralized or misapplied) rules could have gotten there, or if it’s solely looking at the cosmetic or notational similarity to a mixed number (outside of exponents).

I am actually less clear on what led to 1024 = 2^10 from 16 = 2^4. What’s your theory?

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