Integer powers are easy to calculate by repeated application of multiplication. However if a power is not an integer then I always need to use my calculator. How can I calculate a non-integer power without a calculator?
For example, how does one compute 10 raised to 0.90 without a calculator?
The closest I've come to solving the problem is doing fractional power approximations for upper and lower bounds. For example 10 raised to the .31 is greater than 10 raised to the 1/2 but less than 10 raised to the one third
10 raised to the 1/2 is 1/100. 10 raised to the 1/3 is 1/1000. But there is no where near to a good answer................. I think
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