How do you calculate 45 to the power 0.3?

Approximated 3.133.

45^0.3 is the same as finding the 10th root of 45 to the 3rd power.

If you just need the approximate numerical value of an expression like this you can use google. Simply enter: 45^0.3 at the prompt and it will return 3.13302423373

More generally if you lack access to google, or to a calculator that can deal with fractional exponents, then you can make this calculation using logarithms.

log1045 = 1.65...

0.3*log1045 = 0.496...

10^0.496... = 3.1330...

And there are other, numerical methods. Ask again if you're interested.