derivations – Calculate a number raised to the power of a rational number without calculator


so I was asking myself whether you could calculate a number raised to the power of a rational number, e.g. 3^2.5, without a calculator.

My motiviation comes from looking at my calculator and what all those functions like sin, square root… look like. I like it when I know the background off all these. Let’s me understand them better if you know what I mean.

I’m thanking for your answers in advance!!!