how 4 raise to power 0.2 is equal to 1.31

$${{\mathtt{4}}}^{{\mathtt{0.2}}} = {\mathtt{1.319\: \!507\: \!910\: \!772\: \!894\: \!3}}$$

this is already an approximation - if I round it off to 2 dec places I get   1.32

Now

$$4^{0.2}=4^{1/5}=\sqrt[5]{4}$$

Now id the answer really is  1.3195079 then    $$1.3195079^5$$    must equal  4

lets see if it does

$${{\mathtt{1.319\: \!507\: \!9}}}^{{\mathtt{5}}} = {\mathtt{3.999\: \!999\: \!836\: \!713\: \!459\: \!7}}$$    That is close enough to 4 to me