FoM Ch 3 Drill 47 Simplify the following roots

[DanielleT248]

Exponents and roots are my sworn enemy, but I'm determined to figure them out. Okay, once again I can follow the correct answer, but I am having trouble figuring out why my answer is wrong.

Simplify √2^9 + 2^7 - 2^6.

The book factors out 2^6 first then gets √2^6(3^2) then 2^3 x 3 = 8 x 3 = 24. I follow how that works.

I wanted to do it this way and I don't know what's going sideways with my approach:

Combine like terms to get √2^10 = 2^5 = 32.

[esledge]

Roots are so hard to type, too! For anyone else reviewing here, that root sign is "over" the whole expression, so an alternative way to type it is:

Simplify: Square root of [2^9 + 2^7 - 2^6]

So you follow the factoring approach--that's good. In general, if you see addition and subtraction of exponent terms, the only thing you can do is factor out a shared term. On the GMAT, most of the time, that will leave you with manageable terms "left behind," which you will manually add or subtract as just regular numbers, not using exponent rules.

I think what happened to you is that you got that exponent of 10 from doing 9 + 7 - 6 = 10. You would add exponents when you are multiplying terms that have the same base, and you would subtract exponents when you divide terms that have the same base. So, 2^10 would be right if we had been given (2^9)(2^7)/(2^6), but that's not the right exponent move for [2^9 + 2^7 - 2^6].