If you want to find a nth power of a two- digit number, you can modify the Binomial Theorem as follows.

Suppose that you want to find the n th power of the number ab.

Symbols
* denotes the multiplication
^ denotes the power
nCr =(n,r) - combination


(a,b)^n= (n,0)*a^n, (n,1)*a^(n-1) *b, ................, (n,n)*b^n

Ex:

(a,b)^2= a^2, 2*a*b, b^2

(2,5)^2=a^2, 2*a*b, b^2





Similar method can be used to find cube of 25.

(2,5)^3 =[ (2^3 )+ carry], [(3* (2^2)*5) + carry] , [(3* (2)*(5^2) )+ carry], (5^3).

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Subject: to the nth power

Question
I am studying for the Series 66 securities exam and one of the formulas in the text book shows Pn=Po(1+r)n. In the book the n's are smaller than normal and the last one, outside the parenthesese is raised. It has been alot of years since I calculated powers. I think this means to the nth power. If I have examples with specific numbers, how do I calculate the power?
I hope this makes sense.
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Answer
if by this you mean

Pn = Po(1 + r)ª, but instead of ª you have an "n". This is what is known as compound interest.

also i believe "n" is is years, so if you have 6 months, thats .5 years.

Sample of one can be found at http://math.about.com/od/formulas/a/compound.htm

Pn is the result
Po is the Principle or however much money you start out with
r = rate of interest
n = number of years

So if you start out with 100, and the interest rate is 5% and number of years is 5, then

Pn = Po(1 + r)^n
Pn = 100(1 + .05)^5
Pn = 100(1.05)^5
Pn = 100(1.2762815625)
Pn = $127.63

^n is to represent powers, like x^2 = x to the power of 2, or just say "x" squared.


Some problem will give you Pn, and ask for the Po, r, or n. Some compound interest will use "t" for time, instead of "n".



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--Last edited by saucer on 2007-08-22 01:10:04 --