Question

How do you write `c^(3/5)` in radical form?

Answer 1

`root(color(blue)(5))(color(black)(c^color(red)(3)))`

Explanation:

When dealing with exponents which have fractions for exponents we can think of the exponents as having two different parts:

For `x^(color(red)(a)/color(blue)(b))` the exponent of `color(red)(a)/color(blue)(b)` the numerator and denominator each have a meaning.

The numerator `color(red)(a)` is the power of the exponent.

The denominator `color(blue)(b)` is the root of the exponent and what we will use for the radical we creates.

`c^(color(red)(3)/color(blue)(5)) = c^(color(red)(3) * 1/color(blue)(5)) = root(color(blue)(5))(color(black)(c^color(red)(3)))`