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:

$10^0.2= 1.585$