NP Chapter 5 Exponent Strategy Page 106 Problem 22.

[ray_serrano]

I don’t understand how 4^a*(4^2) - 4^a - 4^a*(4^1) becomes 4^a*(4^2 - 4^0 - 4^1), since it seems to violate PEMDAS. Shouldn’t it instead become (4^a * 4^2) -4^a - (4^a * 4^1), since you are supposed to handle multiplication before subtraction?

[andrew.k.john]

Hi Ray.

The missing link is the factoring done to each of the 3 original terms.

Term 1: (4^a)(4^2)
Term 2: (4^a)(4^0)
Term 3: (4^a)(4^1)

Since each term has a common factor of (4^a), we can rewrite the original expression as,

(4^a)(4^2 - 1 - 4) = (4^a)(11).

The factoring does not violate PEMDAS.

Does this make sense?

[esledge]

Well done, Andrew, thanks! I'll further break down that last step in your explanation:

(4^a)[(4^2) - (4^0) - (4^1)] = (4^a)[16 - 1 - 4] = (4^a)(11).