Why does my calculator produce two seemingly different equations?

Question

Or maybe there are two ways this equation can be answered and the different inputs correspond to the calculator's understanding.

Anyway, I have a TI-36x Pro

and when I enter .0179/1x10^-10 I get 1.79x10^-12

But when I enter .0179/10^-10 I get 179000000 or 1.79x10^8

I suspect that when have to enter a number and it must be divided by a number in exponential notation, I cannot enter it as, for example, 1x10^10 but must enter as 10^10.

Does this mean that if I have to divide something say 8x10^-5 I should enter it as 80^-5?

Answer 1

The division is being evaluated first, then the multiplication, because when the operations have the same standing it goes left to right. So in the first case it's dividing by 1, a non-op, and then multiplying by $10^{-10}$, whereas in the latter case it's dividing by $10^{-10}$.

Answer 2

Your calculator interpret the first entry as

$$\frac{.0179}{1} \times 10^{-10}$$

and the second entry as

$$\frac{.0179}{10^{-10}}.$$

Hence, you get different answers.