Why is 10^1.1 = 12.59

Question

I understand why 10^2 = 100. It is just 10x10. 10^3 is 10x10x10. But I can't figure out how exponents that are not whole numbers work. I've spent a lot of time trying to figure this out but I have no idea where these values come from. Why is 10 to the power 1.1 = 12.59???

I can't find anyone who can explain this to me.

I would really appreciate some help.

Answer 1

fractional powers are roots

1/2 power = square root

1/3 power = cube root

1/10 power = tenth root

10^1.1 = 10 x 10^(1/10)= 10 x the 10th power of 10