Math Question: Exponentials

[ilovemcat]

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I encountered a question in one of the Princeton Review passages for Physics which required me to use Poiseuille's Law to calculate the volume flow rate through an artery.

The equation is something like this:

flow rate = pi[(Radius)^4] delta P / 8(viscocity)(length)

Anyways, you can forget all the variables in that equation. My question just focuses on the (Radius)^4 part.

Let's say the radius is 25 x 10^-6 m.
Mathematically, how do we calculate (25x10^-6)^4?

I seen somewhere that we multiply the exponents but what do we do with the 25? If anyone could help, it would be greatly appreciated.

Thanks!

 

[ilovemcat]

Here's the other values for the variables they provided if anyone cares:

pi = approximated to 3
radius = 25 x 10^-6
delta P = 1.2x10^3
viscosity = 2 x 10^-3
length = 10^-3

Answer: 5(25)^3 which honestly I have no idea how they reached that.

 

[Rabolisk]

25*25*25*25 seems awfully tough. But you know what's not tough, 1/4*1/4*1/4*1/4 = 1/256, or 0.25*0.25*0.25*0.25. But each time you convert 25 to .25, you move the decimal point two places, or you multiply by 0.01. So after you calculate 1/256 (which is roughly 1/250 or about 0.004), you have to multiply that answer by 100*100*100*100 or 10^8. 4*10^(-3) * 10^8 = 4*10^5, which is very close to the actual value of 25^4. Combine that with the exponents (4E5 * 1E-24) to get 4E-19.

I have no idea how they got that answer though. What were the units given?

 

[ilovemcat]

25*25*25*25 seems awfully tough. But you know what's not tough, 1/4*1/4*1/4*1/4 = 1/256, or 0.25*0.25*0.25*0.25. But each time you convert 25 to .25, you move the decimal point two places, or you multiply by 0.01. So after you calculate 1/256 (which is roughly 1/250 or about 0.004), you have to multiply that answer by 100*100*100*100 or 10^8. 4*10^(-3) * 10^8 = 4*10^5, which is very close to the actual value of 25^4. Combine that with the exponents (4E5 * 1E-24) to get 4E-19.

I have no idea how they got that answer though. What were the units given?

Holy... I'd probably be too busy flippin out before I did all that lol. Thank you for the explanation.

Their solution didn't have units but since it's flow rate we're solving for, I'm assuming the units are m^3/s. If I get a question like this on the test, I'm just gonna guess and move on lol.