- Exponentiation will multiply powers; e.g., (x^3)^4 = x^12
- Multiplication will add powers; e.g., x^2 * x^3 = x^5
- Addition does a no-op on powers: e.g., 3x^2 + 5x^2 = 8x^2

- Addition does not alter number of places; e.g., 1.2 + 3.4 = 4.6 (1 place)
- Multiplication adds the number of places; e.g., 1.2 * 3.46 = 4.152 (3 places)
- Exponentiation multiplies the number of places; e.g., 1.234^2 = 1.577756 (6 places)

- 1.2 + 3.4

= (1*10^1 + 2*10^-1) + (3*10^1 + 4*10^-1)

= (1*10^1 + 3*10^1) + (2*10^-1 + 4*10^-1)

= 4*10^1 + 6*10^-1

= 4.6

Since the number of decimal places is dictated by the lowest power, if the addition operation 2*10^-1 + 4*10^-1 doesn't change the power (as above), then neither will it change the number of decimal places. And so on and so forth.

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