It comes from the power of 2. 2 = 8/4 so 8/4 + 3/4 is 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?

I’m with matpe.

Multiply, so we add the powers. getting 2and3/4, or 11/4

I now see how the 11/4 came about. Still don’t see how 1024 was arrived at?

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

2 + 3/4 = 11/4 ?

It comes from the power of 2. 2 = 8/4 so 8/4 + 3/4 is 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?

I’m with

matpe.Multiply, so we add the powers. getting 2and3/4, or 11/4

I now see how the 11/4 came about. Still don’t see how 1024 was arrived at?