non whole number exponents, how?

[ShawnD1]

if you have a number like 3^2.5, how is that even possible? the answer is 15.58845........ but how does the calculator get that?

[mireland]

Originally posted by ShawnD1
if you have a number like 3^2.5, how is that even possible? the answer is 15.58845........ but how does the calculator get that?


My head just exploded..:eek:

[Ryan S]

The exact method a calculator uses isn't very important (it's been a while since I've taken Numerical Analysis and it's probably just some algorithm). But here is what it means mathematically:

3^2.5 = 3^(5/2) = square root (3^5)

A fractional exponent means raise the base number to the power given by the number on the top of the fraction and take the root of the number on the bottom of the fraction (or vice versa). So another way to take a square root is to raise a number to a one-half exponent.

[causticVapor]

:p

[Optimus Prime]

We do that in our maths class, even though it will never come up on our exam paper...

x^-1

x^0

bleh, its mad.

x^2/3

[ShawnD1]

Originally posted by Ryan S
A fractional exponent means raise the base number to the power given by the number on the top of the fraction and take the root of the number on the bottom of the fraction (or vice versa). So another way to take a square root is to raise a number to a one-half exponent.

i already knew that i and i knew you would say that... it makes total sense but there is still a problem. lets say you have 4^0.37 so that's the 100th root of 4^37. now how do we find the 100th root of a number?

i'm really sorry that i had such a vague first post there, i woke up at 5AM today and i've been tired all day.