Calculating Gravitational Force with Scientific Notation

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The discussion focuses on calculating gravitational force using scientific notation. The initial calculation provided was incorrect, with the participant arriving at 6.24x10^17. It was pointed out that the participant failed to square the denominator, 6.38x10^6. After clarification, the correct answer was determined to be 9.78x10^0. The thread emphasizes the importance of correctly handling exponents in calculations.
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I need to write this in scientific notation:

(6.67x10^-11)(5.97x10^24)
________________________
( 6.38x10^6)^2

Is
6.24x10^17 right?
 
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Moninder said:
I need to write this in scientific notation:

(6.67x10^-11)(5.97x10^24)
________________________
( 6.38x10^6)^2

Is
6.24x10^17 right?

Not correct.

Please, explain your workings.
 


I did the following:
First took all the numbers, with the x10^# and solved it to 6.24
Now I did the same to the x10^# and got 10^17
 


I figured out the exponents to be x10^1
But can't get the number right
 


Moninder said:
I figured out the exponents to be x10^1
But can't get the number right
Did you square 6.38×106 in the denominator?

It looks as if you didn't.
 


Ok thank you, I figured it out 9.78x10^0 which is the answer
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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