Scientific notation root powers exponents question

[DkEnrgyFrk]

Homework Statement

scientific notation

I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power

Homework Equations

4 . .... ... ... -9
... sq rt of 5.2 X 10

4                        -9
   sq rt of 5.2 X 10

The Attempt at a Solution

The answer I get is +- 8.5 x 10 to the negative 3rd power
but the book is giving me an answer of +- 2.7 x 10 to the -2nd power

I get the +- because it's an even root which means an absolute or + or - number can be squared.
I moved the decimal place 3 places to the right so that the power of -12 can be easily divided by the power of 4.
I tried reversing the decimal place as well so that the power is -8.
I am not getting why I am not coming up with the same answer as the book. I really believe the book is in error.
Can anyone verify either of these and please explain what I am doing wrong if I am incorrect?

Thank you so much in advance.

 

[Mark44]

Homework Statement

scientific notation

I have a problem that displays the 4th root of the square root of 5.2 x 10 to the -9th power

Homework Equations

4 . .... ... ... -9
... sq rt of 5.2 X 10

4                        -9
   sq rt of 5.2 X 10

The Attempt at a Solution

The answer I get is +- 8.5 x 10 to the negative 3rd power
but the book is giving me an answer of +- 2.7 x 10 to the -2nd power

I get the +- because it's an even root which means an absolute or + or - number can be squared.
I moved the decimal place 3 places to the right so that the power of -12 can be easily divided by the power of 4.
I tried reversing the decimal place as well so that the power is -8.
I am not getting why I am not coming up with the same answer as the book. I really believe the book is in error.
Can anyone verify either of these and please explain what I am doing wrong if I am incorrect?

Thank you so much in advance.

Your descriptions are ambiguous. Is this what you mean?
$$\sqrt[4]{\sqrt{5.2~ X~ 10^{-9}}}$$

Or is it this?
$$\sqrt[4]{\sqrt{5.2}}~X~10^{-9}$$

In either case, the fourth root of the square root is the eighth root.