Partial Exponents

[brontesjane]

Good Afternoon,

I am working on solutions in my online chemistry class where my instructor is a facilitator not a teacher so I'm on my own. My problem is:

(3.8*10^9)(10^-5.5)

The first part was easy 3.8*10^9 = 3,800,000,000
Now come the fun part.....

I solved for 10^-5 first, 3,8000,000,000*10^-5 = 38,000

When looking online the problem 38,000*10^-.5 = 12,016.6551086

I don't get it - how do you take a negative "50 percent" of 38,000 and come up with 12,000 and change?!?!?!?

Thank you for any help you can give me.

 

[Deleted member 4993]

Good Afternoon,

I am working on solutions in my online chemistry class where my instructor is a facilitator not a teacher so I'm on my own. My problem is:

(3.8*10^9)(10^-5.5)

The first part was easy 3.8*10^9 = 3,800,000,000
Now come the fun part.....

I solved for 10^-5 first, 3,8000,000,000*10^-5 = 38,000

When looking online the problem 38,000*10^-.5 = 12,016.6551086

I don't get it - how do you take a negative "50 percent" of 38,000 and come up with 12,000 and change?!?!?!? .. That interpretation is not correct

Thank you for any help you can give me.

Another way to look at it:

3.8 * 10⁹ * 10^-5.5 = 3.8 * 10^(9-5.5) = 3.8 * 10^3.5 = 3.8 * 10³ * 10^.5 = 3800 * 3.162278 = 12016.66 ................edited

 

[brontesjane]

Thank you so much! I do have a couple of questions.....

I know that 9-5.5 is 3.5 so should it be 10^3.5? If not how did you arrive at 10^4.5? The other question is how did you get 3.162278?

 

[Quaid]

I know that 9-5.5 is 3.5 so should it be 10^3.5?

Yes.

(Subhotosh may have miscopied some info.)

He intended to post it this way.

3.8 * 10⁹ * 10^-5.5 = 3.8 * 10^(9-5.5) = 3.8 * 10^3.5 = 3.8 * 10³ * 10^.5 = 3800 * 3.162278 = 12016.66

The other question is how did you get 3.162278?

It's staring you in the face! :wink:

You have 3.8*10^3 * 10^0.5 on one side of an equality, and you have 3800 * 3.162278 on the other side.

It's the square root of 10.

 

[Quaid]

38,000*10^-.5 = 12,016.6551086

I don't get it - how do you take a negative "50 percent" of 38,000

That's not how we "take percents". Note that -0.5 is in the exponent position; that's why this situation differs from calculating a percentage.

Remember the property: b^(-x) = 1/b^x

Therefore, 10^(-0.5) = 1/10^(0.5)

Multiplying 38000 by 10^(-0.5) is actually dividing 38000 by the square root of 10.

Cheers

 

[brontesjane]

Thank you again for all of your help.