Exponents and Square Root

[svyessayan]

CAT 4: Holy Exponents, Batman

Square root (1/ (3^0 + 3^-1 + 3^-2 + 3^-3 + 3^-4))

I solved it like this:

Square root [(3 + 9+ 27 + 81)/ 1] = Square root (120)

That was not an answer choice, but I thought the rule was if you have a negative exponent in the denominator, you move to numerator and it becomes positive.

Please advise. Thanks!

[jlucero]

If that's not a trap answer choice, it absolutely should be, because you're doing two smart things, but in the wrong order. Ignoring the square root part of the equation, Let's focus on what happens if you try to flip before you add in an easier fraction:

1/(2^-1 + 2^-1)
*note that 2^-1 is simply one-half

If you add first, you get 1/1 = 1

If you flip the whole equation first, you get (2+2)/1 = 4

That proves that you can't do one of these two methods, since the answers are different. The correct method is to convert the entire denominator into one term, then flip.

[svyessayan]

Thanks Joe!

[tim]

:)