Indices and decimal places 

What is `10^0.2` ?

The way to tackle these problems is (if you can) turn the decimal into a fraction.

So  `10^0.2=10^(2/10)`  

And we now know this equals

`10^(2/10)=(root10\10)^2` 

Which reads

Work out what we have to multiply by itself `10` times to get `10`, then multiply the answer by itself `2` times.

In this case:

`root10\10=1.259`  (see logarithms)

And  `(1.259)^2 = 1.259\times1.259` 

`= 1.585`  

Answer:

`10^0.2= 1.585`