Division fraction with exponents involved.

[RockRan1]

I want to know about the sigh change rule when dividing problems that involve fractions and exponents.
2/(3*10^2/4)
As per fraction rule : a/(b/c)=a*c/1*b
I want to know why when we do the reciprocal the power of 10^8 does not change to 10^-8. When the sign exponential power changes in reciprocal from positive to negative or vice versa .
Please elaborate the rule.

 

[Dr.Peterson]

I want to know about the sigh change rule when dividing problems that involve fractions and exponents.
2/(3*10^2/4)
As per fraction rule : a/(b/c)=a*c/1*b
I want to know why when we do the reciprocal the power of 10^8 does not change to 10^-8. When the sign exponential power changes in reciprocal from positive to negative or vice versa .
Please elaborate the rule.

Please show your work in detail, so we can be sure what you are asking about. It may be best if you provide an image of the work, written as you normally write it. Your "2/(3*10^2/4)" is not entirely clear, and in particular I see no [imath]10^8[/imath] here.

Do you mean [math]2\div(3\times10^2\div4) = \frac{2}{\frac{3\times10^2}{4}}?[/math]

 

[lookagain]

As per fraction rule : a/(b/c)=a*c/1*b

That is incorrect. What you wrote is the equivalent of:

\(\displaystyle \dfrac{a}{(\tfrac{b}{c})} \ = \ \dfrac{a*c}{1}*b\)

Actually, a/(b/c) = a*c/(1*b).

However, you may leave out the asterisks, the grouping symbols,
and the "1" on the right side of the equals sign as in the following:

a/(b/c) = ac/b.

 

[Shiloh]

I would do 2/(3 x 10^2/4) by doing the denominator first. 3/4= 0.75. 10^2= 109 so 3 x 10^2/4= 75.
2/(3 x 10^2/4)= 2/75

Yes, you can write this as 2(4/(3 x 10^2))= 8/3 x 10^-2= 8/300= 2*4/(75*4)= 2/75 again.

 

[lookagain]

10^2= 109 so 3 x 10^2/4= 75.

You have a typo.

\(\displaystyle 10^2 = 100\)

 

[Shiloh]

I need to look again!