Could anyone please help me approximate $\omega^\gamma$.
$\omega=2\pi f$. The range of $f$ is from $0.5 - 200$ and the range of $\gamma$ is from $0.5 - 1$. I tried it to convert to exponential and logarithm like $e^{\gamma log\omega}$ and then expanding it using $e^x$ expansion but I guess its not the best way.
The idea is to be able to approximate the final value with simple multiplications and divisions as I need to implement it on an embedded system. Also, will it help to try to approximate it using binomial or Taylor expansion?
Look up Cordic.
These methods were used in the 70s to compute various functions.
Also, search for "Approximations for Digital Computers" by Hastings. This classic has approximations for, among others, $10^x$ and $\log_{10} x$ which you might be able to compose to do your computions.