Solve for Equation with Powered Fraction

[kayleemom]

I am attempting to complete a finance problem & have forgotten some of my basic algebra rules as it has been over 18 years since I've done algebra.

Here is the problem:

Equation: 2250 X (1 + g)^36= 592,000,000

(1 +g)^36 = 592,000,000/2250
(1 +g)^36 = 263,111
1+g= 263,111 ^ 1/36


The last part is where I get stuck. I do not recall why it becomes 263,111 ^ 1/36 and I can not recall how to solve from here to get the final answer. Your help would be most appreciated.

 

[tkhunny]

Rules of Exponents (Logarithms)

\(\displaystyle \left(a^{m}\right)^{n}\;=\;a^{m*n}\)

\(\displaystyle \left((1+g)^{36}\right)^{\frac{1}{36}}\;=\;1+g\)

\(\displaystyle 1 + g = 263111.111111^{1/36}\)

You'll just need an exponent button for this. Usually \(\displaystyle x^{y}\).

On my Windows 7 v6.1 calculator (set for scientific mode), I did this to solve this problem.

592000000 / 2250 = <this gives 263111.111111>

Without clearing anything...

[x^y] 3 6 [1/x] = <this gives 1.4143582299747127970123220412578]>