FDP Strategy Guide

[Abdulla]

In Action problem #16

8 Root 0.00000256= ?

= (256 * 10^-8 )1/8
= ((256^1/8) *(10^-8)1/8)
= 32* 10^-1
= 3.2

The book's answer 2* 10^-1 = 0.2

please confirm..

[RonPurewal]

In Action problem #16

8 Root 0.00000256= ?

= (256 * 10^-8 )1/8
= ((256^1/8) *(10^-8)1/8)

so far so good.

= 32* 10^-1

no.
raising a number to the 1/8th power means taking the 8th root of that number. in other words, 256^(1/8) is that number which, when raised to the 8th power, yields 256. that's 2.

you put 32, which means you just divided 256 by 8. this is a horrible mistake! it's analogous to thinking that, say, 2^5 is equal to 10.
make sure that you maintain the distinctions between powers/roots and multiplication/division. they are not the same. especially with less familiar functions, such as 8th roots, you need to be en garde.
if you actually know full well that the 8th root of 256 is 2, not 32, and this is just a one-time mistake, then BE AWARE that you make these kinds of mistakes. that extra awareness and vigilance will prevent you from making the same mistakes on g-day.