Exponents question

[drteeth]

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High school was wayyyyyyy too long ago!

How do you do these??

3^1/7 = ?

7^3.19 = ?

1/(2^1/2)

I've forgotten most of this stuff so any help in regard to square roots and these exponents would be greatly appreciated.

Thanks!

 

[Mila]

I think these exponent questions are a little to advanced for the DAT... I've never seen anything like that on any practice or on my DAT, nor have I spoken to anyone who has... That said, you should still definitely have a good understanding of exponents, but more the extend of 8^(-1/3), etc. Good luck!

 

[BenignDMD]

You need a calculator to do the first two, although you can estimate them.

The third one 1/(2^1/2) is easy w/o a calculator. I am assuming you meant to write 1/(2^(1/2)) and that the answers are just simplified, not decimals.

1/(2^(1/2)) - 2^(1/2) is just the square root of 2, so essentially the problem is 1/sqrt2 which is the same as 2^(-1/2).

If you meant to write 1/(2^1/2), then (2^1/2) would be 2/2 = 1. Then 1/1 = 1.

 

[Streetwolf]

3^(1/7) --> Since 7 > 3 the answer is going to be close to 1. In this case it's 1.17 (calculator). I would have guessed somewhere near 1.1-1.2. When you go higher up, ie 5^(1/20) or something, then it will be even closer to 1.

7^(3.19) --> This is the same as (7^3)(7^0.19). So the first number is 343. The second is roughly 7^(1/5) which will be somewhere in the 1.25 - 1.75 range (~1.45 by calculator). So 343 * 1.5 = roughly 510. The actual answer is ~496. Not so far off. On the DAT the answers would be spread out.

But I highly doubt you find these on the DAT.

As for 1/2^(1/2), it's just 1/sqrt(2) = sqrt(2)/2 which is a common trig number. Knowing that sqrt(2) ~ 1.414, you get sqrt(2)/2 ~ 0.707.