Question

What is the simplified form of
`{0.2}^(5)`

Answer 1

You have the following expression:

(0.2)⁵

in order to simplify it, you take into account that 0.2 can be written as 2/10, that is, 0.2=2/10=1/5. Furthermore, you take into account that for a fraction number, exponentiated to some n intenger, you have:

(a/b)ⁿ = aⁿ/bⁿ

Then, you have for (0.2)⁵:

(0.2)⁵ = (2/10)⁵ = (1/5)⁵ = 1⁵/5⁵

1⁵ = 1x1x1x1x1 = 1

5⁵ = 5x5x5x5x5 = 3125

Hence: (0.2)⁵ = 1⁵/5⁵ = 1/3125