Scientific notation root powers exponents question

So you should be dividing the power of -9 by 8, which gives you -1.125. This means the final answer should be in the form of +- a.x 10^1, which is equivalent to +- a.x 10. So the answer should be +- 2.7 x 10^-2, which is the same as what the book gives.
  • #1
DkEnrgyFrk
10
0

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

Code: 
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.
 
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  • #2
DkEnrgyFrk said:

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

Code: 
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?
[tex]\sqrt[4]{\sqrt{5.2~ X~ 10^{-9}}}[/tex]

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

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

What is scientific notation and how is it used in scientific research?

Scientific notation is a way of expressing very large or very small numbers in a concise and standardized format. It is commonly used in scientific research to represent quantities such as distances in space, atomic sizes, and population sizes. Scientific notation is written in the form of a number between 1 and 10 multiplied by a power of 10, which represents the number of decimal places the decimal point must be moved to get the original number.

What are the rules for multiplying and dividing numbers in scientific notation?

When multiplying numbers in scientific notation, you can simply multiply the numbers in front and add the exponents. For example, (4 x 10^3) x (2 x 10^2) = (4 x 2) x 10^(3+2) = 8 x 10^5. When dividing numbers in scientific notation, you can divide the numbers in front and subtract the exponents. For example, (6 x 10^4) / (3 x 10^2) = (6 / 3) x 10^(4-2) = 2 x 10^2.

How do you convert a number from standard form to scientific notation?

To convert a number from standard form (where the decimal point is after the first digit) to scientific notation, you need to move the decimal point to the right or left until there is only one digit to the left of the decimal point. Count the number of places you moved the decimal point and use this as the exponent of 10. If you moved the decimal point to the right, the exponent will be negative. For example, 0.00045 can be written in scientific notation as 4.5 x 10^-4.

What is the difference between a root and a power in scientific notation?

A root is the inverse operation of a power. In scientific notation, a root is represented by using a fractional exponent. For example, the square root of 10 can be written as 10^(1/2) in scientific notation. A power is represented by using a whole number exponent. For example, 10^4 means 10 multiplied by itself 4 times. In scientific notation, this would be written as 10 x 10 x 10 x 10 = 10,000.

How can scientific notation be used to compare very large or very small numbers?

Scientific notation makes it easier to compare numbers that are very large or very small. By comparing the exponents, you can determine which number is larger or smaller. For example, 2.5 x 10^8 is larger than 1.2 x 10^8 because the exponent of 10 is larger. Similarly, 6.4 x 10^-4 is smaller than 2.3 x 10^-3 because the exponent of 10 is smaller.

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